INVERSE MODELLING FOR IDENTIFICATION OF POINT- SOURCE EMISSIONS IN ATMOSPHERE

SARVESH KUMAR SINGH

CENTRE FOR ATMOSPHERIC SCIENCES

INDIAN INSTITUTE OF TECHNOLOGY DELHI

NOVEMBER 2011

© Indian Institute of Technology Delhi (IITD), New Delhi, 2011

Inverse Modelling for Identification of Point-Source

Emissions in Atmosphere

by

Sarvesh Kumar Singh Centre for Atmospheric Sciences

Submitted

in fulfillment of the requirements of the degree of

Doctor of Philosophy

to the

Indian Institute of Technology Delhi November 2011

medicated to I7VIy Parents

Certficate

This is to certify that the thesis entitled "Inverse Modelling for Identification of Point Source

Emissions in Atmosphere" being submitted by Mr. Sarvesh Kumar Singh to the Indian

Institute of Technology Delhi for the award of the degree of DOCTOR OF PHILOSOPHY is a

record of the original bonafide research carried out by him. He has worked under my guidance

and supervision and has fulfilled the requirements for the submission of thesis. The results

presented in this thesis have not been submitted in part or full to any other University or Institute

for award of any degree or diploma.

New Delhi Professor Maithili Sharan

November 2011 Centre for Atmospheric Sciences

Indian Institute of Technology Delhi

Hauz Khas, New Delhi-110 016, India

Acknowfedgements

My PhD years at the Indian Institute of Technology (IIT) Delhi and this thesis had mentorship

from numerous outstanding individuals both from within the institute and outside of it. It is to

these individuals that took part in my study, that my heart felt gratitude and thanks; without their

help, this thesis would not have been a reality.

I would like to express my deepest gratitude to my thesis supervisor, Prof. Maithili

Sharan, Centre for Atmospheric Sciences (CAS), IIT Delhi, for his invaluable guidance,

suggestions and endless encouragement. Prof. Sharan always gave me the freedom to pursue my

own interests and provided me with insightful suggestions and support in developing

independent thinking and research skills. He has been an exceptional mentor and I appreciate

both our professional and personal conversations over the years. The knowledge and wisdom I

have gained from him will forever guide me in education and in life.

It is difficult to overstate my gratitude to Dr. Jean-Pierre Issartel, Centre d'Etudes du

Bouchet, France, for his enthusiasm, inspiration, crucial contribution and his great efforts to

explain things clearly and simply. Throughout my PhD, he provided sound advice, good

teaching, good company and lots of good ideas. I would have been lost without him.

I would like to thank Prof. S. K. Dash, Head, CAS, IIT Delhi, for providing all the

essential facilities in the Centre to carry out the work. I also wish to extend my deep appreciation

to my SRC members; Prof. (Ms.) P. Goyal, Chairman, CRC, Prof. R. P. Sharma, Center for

Energy Studies and Prof. 0. P. Sharma for their constant encouragement and generously sharing

their knowledge and time. I am thankful to Prof. S. K. Dube, Prof. G. Jayaraman, Prof. U. C.

Mohanty, Prof. A. D. Rao, Prof. H. C. Upadhyay, Prof. M. Mohan, Prof. K. AchutaRao, Dr. S.

Dey, Dr. R. C. Raghava and Dr. P. Agarwal for their fruitful suggestions, whole hearted support

and encouragement.

I humbly acknowledge the assistance of whole CAS staff especially L. S. Negi, V. K.

Kaushik, Krishan Kumar, Dataram, Kedari, Mrs. Kusum and Mrs. Saroj Gupta, for their help and

support. I want to acknowledge IITD and MHRD for providing me financial support in the form

of scholarship during my research.

In my daily work, I have been blessed with a friendly and cheerful group of fellow

students. I convey special thanks to my friends Dr. Pramod Kumar, Dr. Mukesh, Sunil and

Anikender with whom I shared my joy and sorrows. Their warm company, unwavering support

in my ups and downs, and helpful suggestions offered at various stages of my Ph.D. work, made

my stay at IIT pleasant and memorable. Now, it is pleasure to mention my colleagues with hearty

thanks: Drs. Jagabandhu, Subrat, Sankalp, Senthil and Swagata, Palash, Liby, Kanhu, Deepak,

Srinivas and Suraj for their support, nice company and sharing various thoughts during the

"Friday break" in the evening. I wish to express thanks to my recent friends Amit, Abhishek,

Dhirender, Himanshu, Ragi, Rati, Amit and Piyush, for their inseparable support and warm

company.

Words fail me to express my appreciation to my wife, Rani whose dedication, love and

persistent confidence in me, has taken the load off my shoulder. I owe her for being unselfishly

let her intelligence, passions, and ambitions collide with mine.

I am indebted to my IIT Roorkee friends especially Amioy, Amit, Nilesh, Navin,

Sandhya, Shailender and Vikas, for providing a stimulating and fun environment in which to

learn and grow. Lastly, I offer my regards and blessings to all of those who supported me in any

respect during the completion of the thesis.

Despite the geographical distance, my family was always nearby. My father made sure I

felt his confidence and encouragement. His advice was consistently timely and useful. Words

cannot completely express my love and gratitude to my family who have supported and

encouraged me through this journey. I would like to thank my parents, sister, Shalini and brother,

Mukesh for their life-long support, everlasting love, and sacrifices, which sustained my interest

in research and motivated me towards the successful completion of this study.

Finally, I thank the almighty God for the passion, strength, perseverance and the

resources to complete this study.

New Delhi Sarvesh Kumar Singh

Abstract Identification of unknown releases in atmosphere is an exigent, practically important and

challenging problem due to national security, industrial hazards, CBR (Chemical, Biological and

Radiological) releases and emergency strategic planning concerns. Since such releases are

unexpected, highly poisonous and impossible to observe or measure directly on site; a direct

identification is not feasible. Therefore, it is required to develop the inverse modelling

techniques for an accurate and fast preliminary identification of the releases from the limited set

of atmospheric concentration measurements.

The primary objective of the thesis is to develop and evaluate the inverse modelling

techniques for retrieval of point source emissions from a set of limited atmospheric concentration

measurements at local scale. The thesis is divided into seven chapters. The first chapter is an

introductory chapter which reviews the earlier works on the inverse modelling techniques along

with their feasibility, applicability, stability and limitations in identifying the releases.

An inversion technique is developed in the second chapter within least square framework

to identify a ground level point emission. An adjoint modelling approach is described to establish

the source-receptor correspondence. This concept is followed in the subsequent chapters for

describing the backward transport of the pollutant. An alternative optimization technique, free

from initialization is proposed for the estimation of release parameters. The technique is

evaluated with the concentration measurements obtained from Indian Institute of Technology

(IIT) Delhi, diffusion experiment in low wind convective conditions.

In chapter 3, the identification of a ground level point emission is addressed within the

assimilative framework of renormalization theory. This theory has been extended for the

identification of a point source based on the property that these are associated with the maximum

of the renormalized estimate computed from the observations. The theory introduces a weight

function and a weight matrix in order to include the natural informations retrieved from the

geometry of the monitoring network and overcomes the limitations encountered in chapter 2. The

theoretical comparisons are highlighted between theories of renormalization and least square.

In general, near surface releases are treated as ground level emissions. Sometimes the

concentrations distribution released from such near surface releases may be sensitive even to a

small height of source and receptor above the ground. Therefore, a renormalization inversion

technique is proposed in chapter 4 for identification of an elevated point release and its

application is investigated in low wind stable conditions. An improved formulation is proposed

for the estimation of source intensity and an estimate is derived for the retrieval errors. The

source reconstruction is carried out using the observations from Idaho diffusion experiment in

low wind stable conditions. The sensitivity studies are carried out to (i) analyze the sensitivity of

the source estimation with respect to signal perturbation caused by the background concentration

of the species in the ambient air and (ii) optimize the number of receptors in a fixed monitoring

network.

The source reconstruction is highly sensitive to the noise in the observations and

representativity errors associated with the dispersion model. In view of this, the minimization of

the model representativity error is addressed in chapter 5 utilizing the modeled concentrations

predicted from an analytical dispersion model and the corresponding measured concentrations

released from an elevated point source in Idaho diffusion experiment in low wind stable

conditions. In general, a linear regression methodology is described for minimizing the model

representativity errors. In view of experimental considerations, continuous functions of

regression coefficients in terms of radial distance from the source are evolved for modifying the

model predicted adjoint functions. A comparison is discussed between source estimates retrieved

in this chapter and in chapter 4 without accounting for model errors.

The identification of single point release is extended to multiple-point releases in chapter

6. The inverse modelling methodology is developed for identifying the multiple-point emissions

releasing similar tracer, in which influence from the various emissions are merged in each

detector's measurement. The identification is addressed from a limited merged set of

atmospheric concentration measurements. The source estimation method is based on two-step

minimization of objective function within the least square framework. A retrieval algorithm is

proposed, free from initialization, for identifying release parameters simultaneously. The

algorithm is further modified and improved by introducing the natural informations retrieved

from the geometry of the monitoring network in terms of weight functions. The methodology has

been successfully applied to identify the two and three simultaneous point emissions from

synthetic measurements generated from the model without noise or with some controlled noise

artificially added and from pseudo real measurements generated from IIT Delhi diffusion

experiment in low wind convective conditions by combining several of single point release runs.

A unique feature of this study is that all the proposed inverse modelling techniques are

evaluated with the real observations. The thesis explores new concepts associated with the

geometry of the monitoring network and emphasizes on a further understanding about the effect

of observation and model representativity errors. The point source reconstruction is exhibited in

the form of source estimate isopleths and further analyzed quantitatively by comparing them

with their corresponding original prescribed source parameters.

Contents

Certificate Acknowledgments Abstract Contents List of Figures List of Tables

1 General Introduction ...........................................................................................................1 1.1 Introduction ................................................................................................................... 2 1.2 Inverse Modelling .......................................................................................................... 5

1.2.1 Source-Receptor Correspondence .....................................................................5 1.2.2 Mathematical Formulation ................................................................................6 1.2.3 Parametric Estimation .......................................................................................7

1.3 Inverse Modelling Techniques ......................................................................................7 1.3.1 Least Square Technique ....................................................................................8 1.3.2 Regularization ...................................................................................................9 1.3.3 Genetic Algorithm ...........................................................................................11 1.3.4 Bayesian Method .............................................................................................13 1 .3.5 Kalman Filter ...................................................................................................16 1.3.6 Concept of Adjoint Modelling .........................................................................19 1.3.7 Back Trajectory Models ...................................................................................21 1.3.8 Renormalization Technique .............................................................................25 1.3.9 Markov Chain Monte Carlo Method ................................................................28 1.3.10 Maximum Entropy on Mean ............................................................................29 1.3.11 Variational Assimilation ..................................................................................32

1.4 Identification of Multiple Point Releases ....................................................................36 1.5 Issues and Limitations .................................................................................................38

1.5.1 Noise in Measurements ...................................................................................39 1.5.2 Selecting a Goodness-of-Fit Measure .............................................................39

1.5.3 Number of Source Parameters ........................................... .............................40

1.5.4 Prior Initialization .............................................................. .............................40

1.5.5 Non-Uniqueness of Solution ...........................................................................40 1.5.6 High Resolution ................................................................. .............................40

1.5.7 Sequential Estimation ........................................................ .............................41

1.5.8 Atmospheric Dispersion Model ......................................... .............................41

1.5.9 Model Representativity Error ............................................. .............................42

1.6 Organization of the Thesis ..........................................................................................42

2 Identification of Single-Point Emission using Classical Least Square Technique .......46 2.1 Introduction .................................................................................................................47 2.2 Methodology ...............................................................................................................49

2.2.1 Source-Receptor Correspondence ...................................................................49

2.2.2 Least Square Formulation ...............................................................................51 2.2.3 Atmospheric Dispersion Model ......................................................................54

2.3 Diffusion Experiment ..................................................................................................56 2.4 Numerical Computations ............................................................................................58

2.5 Results and Discussion ...............................................................................................59

2.5.1 Synthetic Measurements .................................................................................60

2.5.2 Real Measurements .........................................................................................61

2.5.3 Errors in the Retrieval .....................................................................................63

2.6 Advantages and Limitations ........................................................................................64

2.6.1 Advantages ......................................................................................................64

2.6.2 Assumptions/Limitations ................................................................................65

2.6.3 Vertical and Temporal Dimensions ................................................................66

2.6.4 Experimental Data ..........................................................................................66

2.7 Conclusions .................................................................................................................67

3 Identification of Single-Point Emission using Renormalization Technique .................69

3.1 Introduction ................................................................................................................. 70

3.2 Inverse Modelling ........................................................................................................71

3.2.1 Normed Space of Continuous Ground Sources ...............................................72 3.2.2 Computation of the Adjoint Functions ............................................................73

3.2.3 Geometric Weights: The Renormalization ......................................................74

3.2.4 Retrieval of a Point Source ..............................................................................76

3.2.5 Accuracy of Point Source Retrieval ................................................................77

3.3 Diffusion Experiment ..................................................................................................78

3.4 Description of the Computations .................................................................................79

3.5 Results and Discussion ................................................................................................82

3.5.1 Renormalizing Weights and Renormalized Representation ............................84

3.5.2 Synthetic Data ..................................................................................................86

3.5.2.1 Identification of a Point Source ........................................................86

3.5.2.2 Extension of the Estimate Upwind ...................................................86

3.5.3 Real Data .........................................................................................................87

3.5.2.1 Identification of a Point Source ........................................................88

3.5.2.2 Separation of Noise and Signal ........................................................89

3.5.4 Comparison with Least Square Estimation .....................................................91

3.6 Issues and Limitations .................................................................................................93

3.6.1 Renormalized Framework ...............................................................................93

3.6.2 Intensity of the Point Source ...........................................................................95

3.6.3 Feasibility of Source Identification .................................................................96

3.7 Conclusions .................................................................................................................97

4 Identification of an Elevated Point Release: Application to Low Wind Stable Conditions .........................................................................................................................99 4.1 Introduction ...............................................................................................................100 4.2 Inversion Technique ..................................................................................................103

4.2.1 Adjoint Functions ..........................................................................................104 4.2.2 Renormalization ............................................................................................106 4.2.3 Identification of a Point Release from Measurements ..................................108 4.2.4 Estimation of Intensity ..................................................................................110

4.2.5 Estimation of Errors ......................................................................................111

4.3 Diffusion Experiment .................................................................................................112

4.4 Numerical Computations ...........................................................................................115

4.5 Results and Discussion ..............................................................................................118

4.5.1 Synthetic Data ................................................................................................119

4.5.2 Real Data ........................................................................................................121

4.5.3 Extension of the Estimate Upwind .................................................................127

4.5.4 Errors in the Retrieval ....................................................................................128

4.5.5 Sensitivity Analysis ........................................................................................128

4.5.5.1 Background Concentration ..............................................................129

4.5.5.2 Optimizing the Network Design ......................................................131

4.5.6 Issues of Surface/Elevated Releases ...............................................................134

4.6 Limitations ..................................................................................................................135

4.6.1 Data .................................................................................................................135

4.6.2 Representativity Error .....................................................................................135

4.7 Conclusions .................................................................................................................136

5 Minimization of Model Representativity Errors in a Point Source Reconstruction ....138 5.1 Introduction .................................................................................................................13 9

5.2 Methodology ...............................................................................................................141 5.2.1 Representativity Errors Minimization .............................................................141 5.2.2 Estimation of Regression Coefficients ............................................................143

5.2.3 Inverse Modelling ............................................................................................144 5.2.4 Modification of Adjoint Functions ..................................................................144

5.2.5 Experimental Consideration ............................................................................145

5.3 Numerical Computations .............................................................................................146

5.4 Results and Discussion ................................................................................................147

5.5.1 Real Data .........................................................................................................148

5.5.2 Quantitative Comparison of Results with Chapter 4 .......................................151

5.5 Assumptions and Limitations ......................................................................................153

5.6 Conclusions .................................................................................................................154

6 Inverse Modelling for Identification of Multiple-Point Emission Sources ...................156

6.1 Introduction .................................................................................................................157

6.2 Inverse Modelling .......................................................................................................161

6.2.1 Correspondence Between Source and Measurements ....................................161 6.2.2 Identification of Two-Point Sources ...............................................................162

6.2.3 Identification of m-Point Sources ...................................................................165

6.2.4 Weighted Source-Receptor Correspondence ..................................................167

6.2.5 Weighted Approach for Identifying m-point Emission ..................................169

6.3 Preparation of Pseudo Real Measurements ................................................................171

6.4 Numerical Computations ............................................................................................174

6.5 Results and Discussion ...............................................................................................176

6.5.1 Synthetic Measurements .................................................................................176

6.5.2 Pseudo-Real Measurements ............................................................................177

6.5.1.1 Non-Weighted Formulation .............................................................177

6.5.1.2 Weighted Formulation .....................................................................179

6.5.3 Distribution of Weight Function .....................................................................183

6.5.4 Reduction in Computational Time ..................................................................184

6.5.5 Comparative Features of Weighted and Non-Weighted Formulations ...........185

6.5.6 Noisy Synthetic Measurements .......................................................................186

6.5.7 Estimation of Noise Proportion in Pseudo Real Measurements ......................191

6.5.8 Identification of Four Point Sources ................................................................192

6.6 Advantages and Limitations ........................................................................................193

6.6.1 Advantages ......................................................................................................193

6.6.2 Assumptions/Limitations .................................................................................194

6.6.3 Data Limitations ..............................................................................................194

6.7 Conclusions .................................................................................................................195

7 Conclusions and Future Perspectives ...............................................................................197 7.1 Conclusions ...................................................... ...........................................................198

7.2 Limitations and Future Perspectives ................ ...........................................................202

7.2.1 Non-Reactive Tracer Gas ..................... ...........................................................202

7.2.2 Linear Adjoint Modelling ................................................................................202

7.2.3 Known Number of Releases ............................................................................203 7.2.4 Local Scale Point Emission .................. ...........................................................203

7.2.5 Height of Source and Receptors ......................................................................203

7.2.6 Data Availability .............................................................................................203 References .................................................................................................................................205 Bio-Data ....................................................................................................................................235