Turbulence and dispersion flow of radioisotopes in the atmospheric Boundary layer By Sawsan Ibrahiem Mohamed El Said B.sc (physics) Ain Shams University D.M. (Meteorology) Cairo University M.Sc. (Meteorology) Cairo University Thesis Submitted as requirements for degree of Ph.D. in Meteorology TO THE Meteorological and Astronomy Department, Faculty of Science, Cairo University Under Supervision of Prof. Dr. M. M. Abd El-Wahab Prof. Dr. Khaled. S.M. Essa Professor of Meteorological and Professor o f Mathematics and Astronomy Faculty of Science Theoretical Physic Nuclear Cairo University Research Center Atomic Energy Authority (2013) Title of the Ph.D. Thesis Turbulence and dispersion flow of radioisotopes in the atmospheric Boundary layer Name of candidate: Sawsan Ibrahiem Mohamed El Said Submitted to the Cairo University for Degree of Ph.D. in Meteorology Faculty of Science, Meteorological and Astronomy Department, Cairo University (2013) Title of the Ph.D. Thesis Turbulence and dispersion flow of radioisotopes in the atmospheric Boundary layer Name of candidate : Sawsan Ibrahiem Mohamed El Said Submitted to the Cairo University for Degree of Ph.D. in Meteorology Faculty of Science, Meteorological and Astronomy Department . Supervision Committee: Prof. Dr.M. M. Abad El-Wahab Professor of Meteorological, Faculty of Science, Cairo University Prof. Dr. Khaled. S.M. Essa Professor of Mathematics and Theoretical Physic Nuclear Research Center Atomic Energy Authority Assistant Prof. Dr. Mohamed Embay Assistant Professor of Mathematics and Theoretical Physic Nuclear Research Center Atomic Energy Authority Head of the Department of Meteorological and Astronomy , Faculty of Science, Cairo University Prof. Dr.M.YASFE Approval sheet Name of candidate : Sawsan Ibrahiem Mohamed El Said Title of the Ph.D. Thesis Turbulence and dispersion flow of radioisotopes in the atmospheric Boundary layer Submitted to the Faculty of Science, Cairo University Approved by : Prof. Dr.M. M. Abad El-Wahab Professor of Meteorological, Faculty of Science Cairo University Prof. Dr. Khaled. S.M. Essa Professor of Mathematics and Theoretical Physic Nuclear Research Center Atomic Energy Authority Assistant Prof. Dr. Mohamed Embay Assistant Professor of Mathematics and Theoretical Physic Nuclear Research Center Atomic Energy Authority Summary There is an increase in the study of atmospheric pollution and harmful impact on environment, in this work attention was forward to atmospheric diffusion equation to evaluate the concentration pollution with different methods under different stability conditions. The material in the present thesis is organized in six chapters in the following way: Chapter (1), it describe as. In section 1.1, General Introduction, In section 1.2, Turbulence, In section 1.3 , Turbulence of the atmosphere. In section 1.4, Atmospheric stability. In section 1.5, Atmospheric pollution . In section 1.6, Behavior of effluent released to the atmosphere . In section 1.7, Source Types . In section1.8, Atmospheric Dispersion Theories (Modeling). In section1.9.Comparison between Some Models. In section1.10 , The Planetary Boundary Layer. Chapter (2), it describe as: In section 2.1 , Introduction. In section 2.2 , Analytical Method. In section 2.3 , Numerical Method. In section 2.4 , Statistical method. In chapter (3), it describe as : In section 3.1, Introduction. In section 3.2, Analytical solution. In section 3.3, statically methods. Chapter (4), it contain following: In section 4.1, Introduction. In section 4.2, Proposed model structure. In section 4.3, the effective height. In section 4.4, Mathematical technique In section 4. 5, Case study. In section 4.6, Verification . Chapter (5), one can find as: In section 5.1, Introduction. In section 5.2, Gaussian distributions. In section 5.3, Dispersion parameters schemes. In section 5.4, Result and discussion. In section 5.5 Statistical methods. Chapter (6), it can be arranged in the following: In section 6.1, Introduction . In section 6.2, Model formulation. In section 6.3, Results and Discussion. In section 6.4, Statistical method. Some Major Finding of this theses were summarized in published articles (41, 42, 43) ACKNOWLEDGEMENT All gratitude is due God almighty that has ever guided and helped me to bring- forth to light this thesis. I would like to thank my parents and my family for the continuous encouragement and help. My deep appreciation and sincere gratitude are resent to my supervisor, Prof. Dr. Mohamed Magdy Abdel-Wahab, faculty of science Cairo university, for suggestion the interested point of research, supervision and following the following the progress of the work with keep interest, and for his facilities provided to me during the preparation of this thesis, invaluable advice and guidance, for his help and encouragement moral support. I would like to acknowledge my gratitude and sincere thank fullness to my supervisor, Prof. Dr.Khaled Sadek Mohamed Essa for his help and encouragement moral support. I would like to acknowledge my gratitude to Dr. Mokhtar Embaby Assistance professor in Atomic Energy Authority for helpful in this work. اهة آ ام م ا واء و ارد ا ااب وا ا ا ا ا ا ف اي د ن أاه ا رس ء دم أرد اهة أرد اهة ر ل در اآرا ªאú אذאدو אذאدود אذאدو دددאوª د ددقد אذאدאو אذدאªوאطא ذאªوאطא מא¯وאدאو מאªوאطא מאªوאطא אوמא زאوאووאطאذ زאوאوو 2013 ﻤﻠﺨﺹ ﺍﻝﺭﺴﺎﻝﺔ ﻝﻘﺩ ﺫﺍﺩ ﺍﻻﻫﺘﻤﺎﻡ ﺒﺩﺭﺍﺴﺔ ﺍﻨﺘﺸﺎﺭ ﺍﻝﻤﻠﻭﺜﺎﺕ ﺍﻝﺠﻭﻴﺔ ﻭ ﺃﺜﺎﺭﻫﺎ ﺍﻝﻀﺎﺭﺓ ﻋﻠﻰ ﺍﻝﺒﻴﺌﺔ ﻤﻤﺎ ﺩﻓﻌﻨﺎ ﺇﻝﻰ ﺤﺴﺎﺏ ﺘﺭﻜﻴﺯ ﻫﺫﻩ ﺍﻝﻤﻠﻭﺜﺎﺕ ﺒﻁﺭﻕ ﻤﺨﺘﻠﻔﺔ . ﻓﻲ ﺍﻝﻔﺼل ﺍﻷﻭل : : ﺘﻡ ﺩﺭﺍﺴﺔ ﻤﺭﺠﻌﻴﺔ ﻋﻠﻰ ﺍﻨﺘﺸﺎﺭ ﺍﻝﺠﻭﻯ ﻭ ﻤﺘﻐﻴﺭﺍﺕ ﺍﻝﻁﺒﻘﺔ ﺍﻻﻀﻁﺭﺍﺒﻴﺔ ﺍﻝﻤﺨﺘﻠﻔﺔ ﻤﺜل ﺴﺭﻋﺔ ﺍﻝﺭﻴﺎ ﺡ ﻭﻤﻌﺎﻤل ﺍﻝﺘﺸﺘﺕ. ﻭ ﻤﻘﺩﻤﺔ ﻋﻠﻰ ﺍﻷﻀﻁﺭ ﺍ ﺏ ﺍﻝﺠﻭﻯ ﻭﻤﻜﻭﻨﺎﺘﻪ ﻭﺍﻝﻌﻭﺍﻤل ﺍﻝﺘﻰ ﻴﻌﺘﻤﺩ ﻋﻠﻴﻬﺎ ﻭﺩﺭﺍﺴﺔ ﻋﺎﻤﺔ ﻋﻠﻰ ﺍﻷﻨﺘﺸﺎﺭ ﺍﻝﺠﻭﻯ ﻭﺤﺎﻻﺘﻪ ﺍﻝﻤﺨﺘﻠﻔﺔ . ﻭﻤﻘﺩﻤﻪ ﻋﺎﻤﺔ ﻋﻠﻰ ﺍﻝﺘﻠﻭﺙ ﺍﻝﺠﻭﻯ ﻭﺃﻨﻭﺍﻉ ﻤﺤﺘﻠﻔﺔ ﻤﻥ ﺍﻝﻤﺼﺎﺩﺭ ﻭﺍﻝﻨﻤﺎﺫﺝ ﻝﻤﻌﺭﻓﺔ ﺘﺭﻜﻴﺯ ﺍﻝﻤﻠﻭﺜﺎﺕ . ﻭﻗﺩ ﺘﻡ ﺘﻌﺭﻴﻑ ﺃﻨﻭﺍﻉ ﺍﻝﻤﺨﺘﻠﻔﺔ ﺍﻝﻁﺒﻘﺔ ﺍﻝﺤﺩﻴﺔ ﻝﻠﻐﻼﻑ ﺍﻝﺠﻭﻯ. ﻓﻲ ﺍﻝﻔﺼل ﺍﻝﺜﺎﻨﻲ : : ﺘﻡ ﺤل ﻤﻌﺎﺩﻝﺔ ﺍﻷﻨﺘﺸﺎﺭ ﺍﻝﺠﻭﻯ ﻓﻰ ﺃﺘﺠﺎﻫﻴﻥ ﺃﺤﺩﻫﻤﺎ ﻓﻰ ﺃﺘﺠﺎﻩ ﺍﻝﺭﻴﺎﺡ ﻭﻵﺨﺭ ﻓﻰ ﺃﺘﺠﺎﻩ ﺭﺃﺴﻰ ﻭﺫﺍﻝﻙ ﻓﻰ ﺤﺎﻝﺔ ﺍﻝﺜﺒﺎﺕ ﺒﻁﺭﻴﻘﺘﻴﻥ ﻤﺨﺘﻠﻔﺘﻴﻥ ﺃﺤﺩﻫﻤﺎ ﺒﻁﺭﻴﻘﺔ ﺘﺤﻭﻴﻼﺕ ﻻﺒﻼﺱ ﺍﻝﻌﻜﺴﻴﺔ ﻭ ﺍﻷﺨﺭﻯ ﺒﻁﺭﻴﻘﺔ ﻋﺩﺩﻴﺔ ﻤﻊ ﺃﺨﺫ ﻓﻰ ﺍﻷﻋﺘﺒﺎﺭ ﺸﻜﻠﻴﻥ ﻤﺨﺘﻠﻔﻴﻥ ﻝﻤﻌﺎﻤل ﺍﻻﻨﺘﺸﺎﺭ ﺍﻝﺩﻭﺍﻤﻰ ﺒﺤﻴﺙ ﻴﻜﻭﻥ ﻫﺫﺍ ﺍﻝﻤﻌﺎﻤل ﺩﺍﻝﺔ ﻓﻲ ﺍﻝﻤﺴﺎﻓﺔ ﺍﻻﻓﻘﻴﺔ ﻭﻴﻜﻭﻥ ﻫﺫﺍ ﺍﻝﺸﻜﻠﻴﻥ ﺍﺤﺩﻫﻤﺎ ﻓﻰ ﺍﻝﺤﺎﻝﺔ ﺍﻝﻌﺎﺩﻴﺔ ﻝﺠﻭ ﻭﺍﻷﺨﺭ ﻓﻲ ﺍﻝﺤﺎﻝﺔ ﺍﻝﻐﻴﺭ ﻤﺴﺘﻘﺭﺓ ﻝﺠﻭ ﻭﻻﻴﺠﺎﺩ ﺘﺭﻜﻴﺯ ﺍﻝﻤﻠﻭﺜﺎﺕ ﺒﺎﻝﻨﺴﺒﺔ ﻝﻤﻌﺩل ﺍﻷﻨﺒﻌﺎﺙ ﻭﻤﻘﺎﺭﻨﺘﻬﺎ ﺒﺎﻝﺤﺴﺎﻴﺎﺕ ﺍﻝ ﻤﻘﺎﺴﺔ ﻭﻗﺩ ﻭﺠﺩﻨﺎ ﺘﻭﺍﻓﻕ ﺒﻴﻥ ﺤﺴﺎﺒﺎﺘﻨﺎ ﻭ ﺍﻝﺤﺴﺎﺒﺎﺕ ﺍﻝﻤﻘﺎﺴﺔ ﻭﺘﻡ ﻋﻤل ﻁﺭﻕ ﺃﺤﺼﺎﺌﻴﺔ ﻝﻠﻭﺼﻭل ﺍﻝﻰ ﺃﺤﺴﻥ ﻨﻤﻭﺫﺝ ﻤﻊ ﺍﻝﺤﺴﺎﺒﺎﺕ ﺍﻝﻤﻘﺎﺴﺔ . ﻓﻲ ﺍﻝﻔﺼل ﺍﻝﺜﺎﻝﺙ : : ﺘﻡ ﺤل ﻤﻌﺎﺩﻝﺔ ﺍﻻﻨﺘﺸﺎﺭ ﺍﻝﺠﻭﻯ ﻓﻰ ﺍﺘﺠﺎﻫﻴﻥ ( x, z ) ﺫﻭ ﻝﻙ ﻓﻲ ﺤﺎﻝﺔ ﺍﻝﺜﺒﺎﺕ ﺒﻁﺭﻴﻘﺔ ﺘﺤﻭﻴﻼﺕ ﻻﺒﻼﺱ ﺍﻝﻌﻜﺴﻴﺔ ﻤﻊ ﺃﺨﺫ ﻓﻰ ﺍﻻﻋﺘﺒﺎﺭ ﺍﻥ ﻜﻼ ﻤﻥ ﺴﺭﻋﺔ ﺍﻝﺭﻴﺎﺡ ﻭ ﺍﻻﻨﺘﺸﺎﺭ ﺍﻝﺩﻭﺍﻤﻰ ﻴﻌﺘﻤﺩﺍﻥ ﻋﻠﻰ ﺃﻨﺠﺎﻩ ﺍﻝﺭﺍﺴﻲ ﻭﺫﻝﻙ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﺍﻝﺠﻭ ﻤﺘﻌﺎﺩل ﻭﻏﻴﺭ ﻤﺴﺘﻘﺭ ﻻﻴﺠﺎﺩ ﺃﻋﻠﻰ ﺘﺭﻜﻴﺯ ﺴﻁﺢ ﺍﻷﺭﺽ ﻭﻤﻘﺎﺭﻨﺘﻬﺎ ﺒﺎﻝﺤﺴﺎﺒﺎﺕ ﺍﻝﻤﻘﺎﺴﺔ ﻭﻗﺩ ﻭﺠﺩﻨﺎ ﺘﻭﺍﻓﻕ ﺒﻴﻥ ﺤﺴﺎﺒﺎﺘﻨﺎ ﻭ ﺍﻝﺤﺴﺎﺒﺎﺕ ﺍﻝﻤﻘﺎﺴﺔ ﻭﺘﻡ ﻋﻤل ﻁﺭﻕ ﺃﺨﺼﺎﺌﻴﺔ ﻝﻠﻭﺼﻭل ﺇﻝﻰ ﺃﺤﺴﻥ ﻨﻤﻭﺫﺝ ﻤﻊ ﺍﻝﺤﺴﺎﺒﺎﺕ ﺍﻝﻤﻘﺎﺴﺔ . ﻓﻲ ﺍﻝﻔﺼل ﺍﻝﺭﺍﺒﻊ : ﺘﻡ ﻋﻤل ﻋﻤل ﻨﻤﻭﺫﺝ ﺒﺴﻴﻁ ﻝﺤﺴﺎﺏ ﺘﺭﻜﻴﺯ ﺍﻝﻤﻠﻭﺜﺎﺕ ﻭﺫﻝﻙ ﺒﺎﻋﺘﺒﺎﺭ ﺍﻥ ﺴﺭﻋﺔ ﺍﻝﺭﻴﺎﺡ ﺘﻌﺘﻤﺩ ﻋﻠﻰ ﻜﻼ ﻤﻥ ﺍﻝﻘﻭﺓ ﺍﻻﺴﻴﺔ ﻭﺍﻝﻠﻭﻏﺎﺭﺘﻤﻴﺔ ﻤﻌﺎ ﻭﺘﻡ ﻤﻘﺎﺭﻨﺔ ﺍﻝﺘﺭﻜﻴﺯﺍﺕ ﺍﻝﺘﻰ ﺘﻡ ﺍﻝﻭﺼﻭل ﺍﻝﻴﻬﺎ ﻤﻊ ﺍﻝﺤﺴﺎﺒﺎﺕ ﻗﺩ ﺤﺴﺒﺕ ﻤﻥ ﻗﺒل ﻓﻭﺠﺩﻨﺎ ﺘﻁﺎﺒﻕ ﻫﺫﺍ ﺍﻝﻨﻤﻭﺯﺝ ﻭ ﺍﻝ ﻨﻤﺎﺫﺝ ﺍﻝﺴﺎﺒﻘﺔ ﻓﻰ ﺤﺎﻻﺕ ﺍﻝﺠﻭ ﺍﻝﻤﺨﺘﻠﻔﺔ . ﻓﻲ ﺍﻝﻔﺼل ﺍﻝﺨﺎﻤﺱ: ﺘﻡ ﺤﺴﺎﺏ ﺘﺭﻜﻴﺯﺍﺕ ﺍﻝﻨﻅﺎﺌﺭ ﺍﻝﻤﺸﻌﺔ ﻝﻌﻨﺎﺼﺭ ( I131 , I 135 ,I 133 to and Cs 137 ) ﻭﺫﻝﻙ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﺸﻜﺎل ﻤﺨﺘﻠﻔﺔ ﻝﻤﻌﺎﻤﻼﺕ ﺍﻝﺘﺸﺘﺕ (Power law, standard method, Irwin method and Briggs method) ﻭﺘﻡ ﺍﻝﺘﻌﻭﻴﺽ ﺒﻬﻤﺎ ﻓﻰ ﻤﻌﺎﺩﻝﺔ ﺠﺎﻭﺱ ﻭﺘﻡ ﺍﻀﺎﻓﺔ ﻤﻌﺎﻤل ﺍﻻﻀﻤﺤﻼل ﻝﻠﻌﻨﺎﺼﺭ ﺍﻝﻤﺸﻌﺔ ﻭﺘﻡ ﺤﺴﺎﺏ ﺍﻝﻨﺸﺎﻁ ﺍﻻﺸﻌﺎﻋﻰ ﻭﻤﻘﺎﺭﻨﺘﻬﻤﺎ ﻤﻊ ﺘﺭﻜﻴﺯﺍﺕ ﻤﻘﺎﺴﺔ ﻓﻭﺠﺩﻨﺎ ﻤﻁﺎﺒﻘﺔ . ﻭﺘﻡ ﻋﻤل ﻨﻤﻭﺯﺝ ﺍﺤﺼﺎﺌﻰ ﻻﻴﺠﺎﺩ ﺍﺤﺴﻥ ﺘﺭﻜﻴﺯ. ﻓﻲ ﺍﻝﻔﺼل ﺍﻝﺴﺎﺩﺱ : ﺘﻡ ﺍﺸﺘﻘﺎﻕ ﺼﻭﺭﺓ ﺠﺩﻴﺩﺓ ﻝﻤﻌﺎﻤﻠﻲ ﺍﻝﺘﺸﺘﺕ ﺍﻝﻤﺴﺘﻌﺭﺽ ﻭﺍﻝﺭﺍﺴﻲ ﻭ ﺘﻡ ﺍﺴﺘﺨﺩﻤﻬﺎ ﻓﻲ ﻤﻌ ﺎﺩﻝﺔ ﺠﺎﻭﺱ ﻋﻠﻰ ﺴﻁﺢ ﺍﻷﺭﺽ ﻭﻋﻠﻰ ﺨﻁ ﺍﻝﻤﺭﻜﺯ ﻭﺍﺴﺘﺨﺩﻤﻨﺎ ﺒﻴﺎﻨﺎﺕ ﻤﻘﺎﺴﺔ ﻤﻥ ﻗﺒل ﻝﻠﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﺍﻝﻨﻤﻭﺫﺝ ﺍﻝﺫﻱ ﺘﻡ ﺍﺸﺘﻘﺎﻗﻪ ﻭﻭﺠﺩﻨﺎ ﺘﻁﺎﺒﻕ ﺒﻴﻥ ﺍﻝﺒﻴﺎﻨﺎﺕ ﺍﻝﻤﻘﺎﺴﺔ ﻭﺍﻝﻤﺤﺴﻭﺒﺔ . Contents Page ACKNNTOWLEDGEME Abstract ABBREVIATIONS Chapter I Review study on atmospheric diffusion and dispersion parameters of atmospheric boundary layer 1.1 General Overview 1 1.2 Turbulence 4 1.2.1 Description of turbulence 5 1.2.2 Turbulent flux 5 1.2.3 Parameterization of turbulence 9 1.3 Turbulence of the atmosphere 11 1.3.1 Types of Turbulences. 11 1.3.2 Turbulence diffusion 12 1.4 Atmospheric stability 12 1. 5 Atmospheric pollution. 16 1-6- Behavior of effluent released to the atmosphere 17 1.7 Source Types 18 1.8 Atmospheric Dispersion Theories (Modeling). 19 1.8.1- Eulerian models 20 1.8.2- Lagrange models 23 1.8.3 Gaussian plume and puff models 23 1.8.4-Ground Dispersion Formula 24 1.8.5-Plume rise 26 1.9- Comparison between Some Models 28 1.9.1- Simplified methods 28 1.9.2- Pasquill-Gifford type methods 28 1.9.3- Temperature lapse rate method 29 1.9.4- Wind fluctuation method 29 1.9.5. The effect of friction 31 1.10 The Planetary Boundary Layer 31 1.10 .1 Definition the Planetary Boundary Layer 31 1.10 .2 .The Depth the Planetary Boundary Layer 32 1.10 .3 .The types of the Planetary Boundary layer 32 1.10 .3.1 Definition the surface layer 32 1.10 .3.2 Definition the Ekman layer 32 1 1.11. Model evaluation methodologies 34 1.12. The objective of this study 34 Page Chapter II Analytical and Numerical Solutions of Crosswind Integrated Concentration by using Different eddy diffusivities methods 2.1-Introduction 37 2.2- Analytical Method 39 2.3 Numerical Method 42 2.4 -Statistical method 43 Chapter III Maximum integrated ground level concentration under two stability classes 3.1-Introduction 56 3.2-Analytical solution 57 3.2 a In neutral case 57 3.2 .b In unstable case 62 3.3 Statically method 70 Chapter IV A Simple Model for Pollutant Diffusion Emitted from a Point Source under different Atmospheric Conditions 4-1-Introduction 71 4.2-Proposed model and its components 72 4-3 The effective height 73 4.4 -Mathematical technique 73 4.