Atmospheric Chemistry and Physics: From Air Pollut ion to Climate Change, Third Edition

Preface to the First Edition xxiii
Preface to the Third Edition xxv

PART I | The Atmosphere and Its Constituents

Chapter 1 | The Atmosphere 3
1.1 History and Evolution of Earth s Atmosphere 3
1.2 Climate 5
1.3 Layers of the Atmosphere 5
1.4 Pressure in the Atmosphere 7
1.4.1 Units of Pressure 7
1.4.2 Variation of Pressure with Height in the Atmosphere 7
1.5 Temperature in the Atmosphere 10
1.6 Expressing the Amount of a Substance in the Atmosphere 10
1.7 Airborne Particles 14
1.8 Spatial and Temporal Scales of Atmospheric Processes 14
Problems 16
References 17

Chapter 2 | Atmospheric Trace Constituents 18
2.1 Atmospheric Lifetime 19
2.2 Sulfur–Containing Compounds 23
2.2.1 Dimethyl Sulfide (CH3SCH3) 26
2.2.2 Carbonyl Sulfide (OCS) 26
2.2.3 Sulfur Dioxide (SO2) 27
2.3 Nitrogen–Containing Compounds 27
2.3.1 Nitrous Oxide (N2O) 28
2.3.2 Nitrogen Oxides (NOx=NO+NO2) 29
2.3.3 Reactive Odd Nitrogen (NOy) 30
2.3.4 Ammonia (NH3) 31
2.3.5 Amines 32
2.4 Carbon–Containing Compounds 32
2.4.1 Classification of Hydrocarbons 32
2.4.2 Methane 34
2.4.3 Volatile Organic Compounds 36
2.4.4 Biogenic Hydrocarbons 36
2.4.5 Carbon Monoxide 39
2.4.6 Carbon Dioxide 40
2.5 Halogen–Containing Compounds 40
2.5.1 Methyl Chloride (CH3Cl) 42
2.5.2 Methyl Bromide (CH3Br) 42
2.6 Atmospheric Ozone 44
2.7 Particulate Matter (Aerosols) 47
2.7.1 Stratospheric Aerosol 48
2.7.2 Chemical Components of Tropospheric Aerosol 48
2.7.3 Cloud Condensation Nuclei (CCN) 49
2.7.4 Sizes of Atmospheric Particles 49
2.7.5 Carbonaceous Particles 51
2.7.6 Mineral Dust 53
2.7.7 Biomass Burning 53
2.7.8 Summary of Atmospheric Particulate Matter 54
2.8 Mercury 55
2.9 Emission Inventories 55
Appendix 2.1 US Air Pollution Legislation 56
Appendix 2.2 Hazardous Air Pollutants (Air Toxics) 57
Problems 59
References 61

PART II | Atmospheric Chemistry

Chapter 3 | Chemical Kinetics 69
3.1 Order of Reaction 69
3.2 Theories of Chemical Kinetics 71
3.2.1 Collision Theory 71
3.2.2 Transition State Theory 74
3.2.3 Potential Energy Surface for a Bimolecular Reaction 75
3.3 The Pseudo–Steady–State Approximation 76
3.4 Reactions of Excited Species 77
3.5 Termolecular Reactions 78
3.6 Chemical Families 81
3.7 Gas Surface Reactions 83
Problems 84
References 87

Chapter 4 | Atmospheric Radiation and Photochemistry 88
4.1 Radiation 88
4.2 Radiative Flux in the Atmosphere 91
4.3 Beer Lambert Law and Optical Depth 93
4.4 Actinic Flux 95
4.5 Atmospheric Photochemistry 97
4.6 Absorption of Radiation by Atmospheric Gases 100
4.7 Absorption by O2 and O3 105
4.8 Photolysis Rate as a Function of Altitude 109
4.9 Photodissociation of O3 to Produce O and O(1D) 112
4.10 Photodissociation of NO2 114
Problems 117
References 117

Chapter 5 | Chemistry of the Stratosphere 119
5.1 Chapman Mechanism 122
5.2 Nitrogen Oxide Cycles 129
5.2.1 Stratospheric Source of NOx from N2O 129
5.2.2 NOx Cycles 131
5.3 HOx Cycles 134
5.4 Halogen Cycles 139
5.4.1 Chlorine Cycles 140
5.4.2 Bromine Cycles 143
5.5 Reservoir Species and Coupling of the Cycles 144
5.6 Ozone Hole 146
5.6.1 Polar Stratospheric Clouds (PSCs) 149
5.6.2 PSCs and the Ozone Hole 150
5.6.3 Arctic Ozone Hole 153
5.7 Heterogeneous (Nonpolar) Stratospheric Chemistry 155
5.7.1 The Stratospheric Aerosol Layer 155
5.7.2 Heterogeneous Hydrolysis of N2O5 155
5.7.3 Effect of Volcanoes on Stratospheric Ozone 160
5.8 Summary of Stratospheric Ozone Depletion 162
5.9 Transport and Mixing in the Stratosphere 165
5.10 Ozone Depletion Potential 167
Problems 168
References 173

Chapter 6 | Chemistry of the Troposphere 175
6.1 Production of Hydroxyl Radicals in the Troposphere 176
6.2 Basic Photochemical Cycle of NO2, NO, and O3 179
6.3 Atmospheric Chemistry of Carbon Monoxide 181
6.3.1 Low–NOx Limit 183
6.3.2 High–NOx Limit 184
6.3.3 Ozone Production Efficiency 184
6.3.4 Theoretical Maximum Yield of Ozone from CO Oxidation 188
6.4 Atmospheric Chemistry of Methane 188
6.5 The NOx and NOy Families 192
6.5.1 Daytime Behavior 192
6.5.2 Nighttime Behavior 193
6.6 Ozone Budget of the Troposphere and Role of NOx 195
6.6.1 Ozone Budget of the Troposphere 195
6.6.2 Role of NOx 195
6.6.3 Global Hydroxyl Radical Budget 197
6.7 Tropospheric Reservoir Molecules 203
6.7.1 H2O2, CH3OOH, and Hydroperoxides 203
6.7.2 Nitrous Acid (HONO) 204
6.7.3 Peroxyacyl Nitrates (PANs) 204
6.8 Relative Roles of VOC and NOx in Ozone Formation 208
6.8.1 Importance of the VOC/NOx Ratio 208
6.8.2 Ozone Isopleth Plot 209
6.8.3 Weekend Ozone Effect 211
6.9 Simplified Organic/NOx Chemistry 212
6.10 Chemistry of Nonmethane Organic Compounds in the Troposphere 214
6.10.1 Alkanes 215
6.10.2 Alkenes 222
6.10.3 Aromatics 228
6.10.4 Aldehydes 230
6.10.5 Ketones 230
6.10.6 Ethers 231
6.10.7 Alcohols 231
6.10.8 Tropospheric Lifetimes of Organic Compounds 232
6.11 Atmospheric Chemistry of Biogenic Hydrocarbons 233
6.11.1 Atmospheric Chemistry of Isoprene 233
6.11.2 Monoterpenes ( –Pinene) 241
6.12 Atmospheric Chemistry of Reduced Nitrogen Compounds 244
6.12.1 Amines 245
6.12.2 Nitriles 246
6.12.3 Nitrites 246
6.13 Atmospheric Chemistry (Gas Phase) of Sulfur Compounds 246
6.13.1 Sulfur Oxides 246
6.13.2 Reduced Sulfur Compounds (Dimethyl Sulfide) 247
6.14 Tropospheric Chemistry of Halogen Compounds 249
6.14.1 Chemical Cycles of Halogen Species 249
6.14.2 Tropospheric Chemistry of CFC Replacements: Hydrofluorocarbons (HFCs) and Hydrochlorofluorocarbons (HCFCs) 251
6.15 Atmospheric Chemistry of Mercury 253
Appendix 6 Organic Functional Groups 254
Problems 256
References 259

Chapter 7 | Chemistry of the Atmospheric Aqueous Phase 265
7.1 Liquid Water in the Atmosphere 265
7.2 Absorption Equilibria and Henry s Law 268
7.3 Aqueous–Phase Chemical Equilibria 271
7.3.1 Water 271
7.3.2 Carbon Dioxide Water Equilibrium 272
7.3.3 Sulfur Dioxide Water Equilibrium 274
7.3.4 Ammonia Water Equilibrium 278
7.3.5 Nitric Acid Water Equilibrium 280
7.3.6 Equilibria of Other Important Atmospheric Gases 281
7.4 Aqueous–Phase Reaction Rates 284
7.5 S(IV) S(VI) Transformation and Sulfur Chemistry 286
7.5.1 Oxidation of S(IV) by Dissolved O3 286
7.5.2 Oxidation of S(IV) by Hydrogen Peroxide 289
7.5.3 Oxidation of S(IV) by Organic Peroxides 290
7.5.4 Uncatalyzed Oxidation of S(IV) by O2 291
7.5.5 Oxidation of S(IV) by O2 Catalyzed by Iron and Manganese 291
7.5.6 Comparison of Aqueous–Phase S(IV) Oxidation Paths 293
7.6 Dynamic Behavior of Solutions with Aqueous–Phase Chemical Reactions 295
7.6.1 Closed System 296
7.6.2 Calculation of Concentration Changes in a Droplet with Aqueous–Phase Reactions 298
Appendix 7.1 Thermodynamic and Kinetic Data 301
Appendix 7.2 Additional Aqueous–Phase Sulfur Chemistry 305
7A.1 S(IV) Oxidation by the OH Radical 305
7A.2 Oxidation of S(IV) by Oxides of Nitrogen 308
7A.3 Reaction of Dissolved SO2 with HCHO 309
Appendix 7.3 Aqueous–Phase Nitrite and Nitrate Chemistry 311
7A.4 NOx Oxidation 311
7A.5 Nitrogen Radicals 311
Appendix 7.4 Aqueous–Phase Organic Chemistry 312
Appendix 7.5 Oxygen and Hydrogen Chemistry 313
Problems 314
References 317

PART III | Aerosols

Chapter 8 | Properties of the Atmospheric Aerosol 325
8.1 The Size Distribution Function 325
8.1.1 The Number Distribution nN(Dp) 328
8.1.2 The Surface Area, Volume, and Mass Distributions 330
8.1.3 Distributions Based on ln Dp and log Dp 331
8.1.4 Relating Size Distributions Based on Different Independent Variables 333
8.1.5 Properties of Size Distributions 334
8.1.6 Definition of the Lognormal Distribution 335
8.1.7 Plotting the Lognormal Distribution 338
8.1.8 Properties of the Lognormal Distribution 339
8.2 Ambient Aerosol Size Distributions 342
8.2.1 Urban Aerosols 343
8.2.2 Marine Aerosols 344
8.2.3 Rural Continental Aerosols 347
8.2.4 Remote Continental Aerosols 348
8.2.5 Free Tropospheric Aerosols 348
8.2.6 Polar Aerosols 349
8.2.7 Desert Aerosols 349
8.3 Aerosol Chemical Composition 352
8.4 Spatiotemporal Variation 354
Problems 357
References 359

Chapter 9 | Dynamics of Single Aerosol Particles 362
9.1 Continuum and Noncontinuum Dynamics: the Mean Free Path 362
9.1.1 Mean Free Path of a Pure Gas 363
9.1.2 Mean Free Path of a Gas in a Binary Mixture 365
9.2 The Drag on a Single Particle: Stokes Law 368
9.2.1 Corrections to Stokes Law: the Drag Coefficient 371
9.2.2 Stokes Law and Noncontinuum Effects: Slip Correction Factor 371
9.3 Gravitational Settling of an Aerosol Particle 372
9.4 Motion of an Aerosol Particle in an External Force Field 376
9.5 Brownian Motion of Aerosol Particles 376
9.5.1 Particle Diffusion 379
9.5.2 Aerosol Mobility and Drift Velocity 381
9.5.3 Mean Free Path of an Aerosol Particle 384
9.6 Aerosol and Fluid Motion 385
9.6.1 Motion of a Particle in an Idealized Flow (90° Corner) 386
9.6.2 Stop Distance and Stokes Number 387
9.7 Equivalent Particle Diameters 388
9.7.1 Volume Equivalent Diameter 388
9.7.2 Stokes Diameter 390
9.7.3 Classical Aerodynamic Diameter 391
9.7.4 Electrical Mobility Equivalent Diameter 393
Problems 393
References 394

Chapter 10 | Thermodynamics of Aerosols 396
10.1 Thermodynamic Principles 396
10.1.1 Internal Energy and Chemical Potential 396
10.1.2 The Gibbs Free Energy G 398
10.1.3 Conditions for Chemical Equilibrium 400
10.1.4 Chemical Potentials of Ideal Gases and Ideal–Gas Mixtures 402
10.1.5 Chemical Potential of Solutions 404
10.1.6 The Equilibrium Constant 408
10.2 Aerosol Liquid Water Content 409
10.2.1 Chemical Potential of Water in Atmospheric Particles 411
10.2.2 Temperature Dependence of the DRH 412
10.2.3 Deliquescence of Multicomponent Aerosols 415
10.2.4 Crystallization of Single– and Multicomponent Salts 419
10.3 Equilibrium Vapor Pressure Over a Curved Surface: the Kelvin Effect 419
10.4 Thermodynamics of Atmospheric Aerosol Systems 423
10.4.1 The H2SO4 H2O System 423
10.4.2 The Sulfuric Acid Ammonia Water System 427
10.4.3 The Ammonia Nitric Acid Water System 430
10.4.4 The Ammonia Nitric Acid Sulfuric Acid Water System 434
10.4.5 Other Inorganic Aerosol Species 439
10.4.6 Organic Aerosol 440
10.5 Aerosol Thermodynamic Models 440
Problems 442
References 443

Chapter 11 | Nucleation 448
11.1 Classical Theory of Homogeneous Nucleation: Kinetic Approach 449
11.1.1 The Forward Rate Constant i 452
11.1.2 The Reverse Rate Constant i 453
11.1.3 Derivation of the Nucleation Rate 453
11.2 Classical Homogeneous Nucleation Theory: Constrained Equilibrium Approach 457
11.2.1 Free Energy of i–mer Formation 457
11.2.2 Constrained Equilibrium Cluster Distribution 459
11.2.3 The Evaporation Coefficient i 461
11.2.4 Nucleation Rate 461
11.3 Recapitulation of Classical Theory 464
11.4 Experimental Measurement of Nucleation Rates 465
11.4.1 Upward Thermal Diffusion Cloud Chamber 466
11.4.2 Fast Expansion Chamber 466
11.4.3 Turbulent Mixing Chambers 467
11.5 Modifications of the Classical Theory and More Rigorous Approaches 467
11.6 Binary Homogeneous Nucleation 468
11.7 Binary Nucleation in the H2SO4 H2O System 473
11.8 Nucleation on an Insoluble Foreign Surface 475
11.9 Ion–Induced Nucleation 478
11.10 Atmospheric New–Particle Formation 480
11.10.1 Molecular Constituency of New Particles 481
11.10.2 New–Particle Growth Rates 482
11.10.3 CLOUD Studies of Atmospheric Nucleation 482
11.10.4 Atmospheric Nucleation by Organic Species 487
Appendix 11 The Law of Mass Action 487
Problems 489
References 490

Chapter 12 | Mass Transfer Aspects of Atmospheric Chemistry 493
12.1 Mass and Heat Transfer to Atmospheric Particles 493
12.1.1 The Continuum Regime 493
12.1.2 The Kinetic Regime 497
12.1.3 The Transition Regime 497
12.1.4 The Accommodation Coefficient 500
12.2 Mass Transport Limitations in Aqueous–Phase Chemistry 503
12.2.1 Characteristic Time for Gas–Phase Diffusion to a Particle 505
12.2.2 Characteristic Time to Achieve Equilibrium at the Gas Liquid Interface 506
12.2.3 Characteristic Time of Aqueous Dissociation Reactions 508
12.2.4 Characteristic Time of Aqueous–Phase Diffusion in a Droplet 510
12.2.5 Characteristic Time for Aqueous–Phase Chemical Reactions 511
12.3 Mass Transport and Aqueous–Phase Chemistry 511
12.3.1 Gas–Phase Diffusion and Aqueous–Phase Reactions 512
12.3.2 Aqueous–Phase Diffusion and Reaction 514
12.3.3 Interfacial Mass Transport and Aqueous–Phase Reactions 515
12.3.4 Application to the S(IV) Ozone Reaction 517
12.3.5 Application to the S(IV) Hydrogen Peroxide Reaction 519
12.3.6 Calculation of Aqueous–Phase Reaction Rates 520
12.3.7 An Aqueous–Phase Chemistry/Mass Transport Model 525
12.4 Mass Transfer to Falling Drops 526
12.5 Characteristic Time for Atmospheric Aerosol Equilibrium 527
12.5.1 Solid Aerosol Particles 528
12.5.2 Aqueous Aerosol Particles 529
Appendix 12 Solution of the Transient Gas–Phase Diffusion Problem: Equations (12.4) (12.7) 532
Problems 533
References 535

Chapter 13 | Dynamics of Aerosol Populations 537
13.1 Mathematical Representations of Aerosol Size Distributions 537
13.1.1 Discrete Distribution 537
13.1.2 Continuous Distribution 538
13.2 Condensation 538
13.2.1 The Condensation Equation 538
13.2.2 Solution of the Condensation Equation 540
13.3 Coagulation 544
13.3.1 Brownian Coagulation 544
13.3.2 The Coagulation Equation 551
13.3.3 Solution of the Coagulation Equation 553
13.4 The Discrete General Dynamic Equation 557
13.5 The Continuous General Dynamic Equation 558
Appendix 13.1 Additional Mechanisms of Coagulation 560
13A.1 Coagulation in Laminar Shear Flow 560
13A.2 Coagulation in Turbulent Flow 560
13A.3 Coagulation from Gravitational Settling 561
13A.4 Brownian Coagulation and External Force Fields 562
Appendix 13.2 Solution of (13.73) 567
Problems 568
References 571

Chapter 14 | Atmospheric Organic Aerosols 573
14.1 Chemistry of Secondary Organic Aerosol Formation 574
14.1.1 Oxidation State of Organic Compounds 576
14.1.2 Generation of Highly Oxygenated Species by Autoxidation 579
14.2 Volatility of Organic Compounds 582
14.3 Idealized Description of Secondary Organic Aerosol Formation 583
14.3.1 Noninteracting Secondary Organic Aerosol Compounds 583
14.3.2 Formation of Binary Ideal Solution with Preexisting Aerosol 586
14.3.3 Formation of Binary Ideal Solution with Other Organic Vapor 588
14.4 Gas Particle Partitioning 590
14.4.1 Gas Particle Equilibrium 590
14.4.2 Effect of Aerosol Water on Gas–Particle Partitioning 594
14.5 Models of SOA Formation and Evolution 596
14.5.1 The Volatility Basis Set 597
14.5.2 Two–Dimensional SOA Models 603
14.6 Primary Organic Aerosol 605
14.7 The Physical State of Organic Aerosols 608
14.8 SOA Particle–Phase Chemistry 610
14.8.1 Particle–Phase Accretion Reactions 612
14.8.2 Heterogeneous Gas–Aerosol Reactions 612
14.9 Aqueous–Phase Secondary Organic Aerosol Formation 615
14.9.1 Gas– versus Aqueous–Phase Routes to SOA 616
14.9.2 Sources of OH Radicals in the Aqueous Phase 618
14.9.3 Glyoxal as a Source of aqSOA 619
14.10 Estimates of the Global Budget of Atmospheric Organic Aerosol 622
14.10.1 Estimate Based on Total VOC Emissions 622
14.10.2 Sulfate Lifetime and Ratio of Organic to Sulfate 622
14.10.3 Atmospheric Burden and Lifetime of SOA 623
14.10.4 Satellite Measurements 623
Problems 623
References 626

Chapter 15 | Interaction of Aerosols with Radiation 633
15.1 Scattering and Absorption of Light by Small Particles 633
15.1.1 Rayleigh Scattering Regime 638
15.1.2 Geometric Scattering Regime 640
15.1.3 Scattering Phase Function 640
15.1.4 Extinction by an Ensemble of Particles 640
15.2 Visibility 644
15.3 Scattering, Absorption, and Extinction Coefficients From Mie Theory 647
15.4 Calculated Visibility Reduction Based on Atmospheric Data 651
Appendix 15 Calculation of Scattering and Extinction Coefficients by Mie Theory 654
Problems 654
References 656

PART IV | Physical and Dynamic Meteorology, Cloud Physics, and Atmospheric Diffusion

Chapter 16 | Physical and Dynamic Meteorology 661
16.1 Temperature in the Lower Atmosphere 661
16.2 Atmospheric Stability 665
16.3 The Moist Atmosphere 670
16.3.1 The Gas Constant for Moist Air 671
16.3.2 Level of Cloud Formation: The Lifting Condensation Level 671
16.3.3 Dew–point and Wet–Bulb Temperatures 673
16.3.4 The Moist Adiabatic Lapse Rate 675
16.3.5 Stability of Moist Air 679
16.3.6 Convective Available Potential Energy (CAPE) 680
16.3.7 Thermodynamic Diagrams 681
16.4 Basic Conservation Equations for the Atmospheric Surface Layer 683
16.4.1 Turbulence 687
16.4.2 Equations for the Mean Quantities 688
16.4.3 Mixing–Length Models for Turbulent Transport 690
16.5 Variation of Wind with Height in the Atmosphere 692
16.5.1 Mean Velocity in the Adiabatic Surface Layer over a Smooth Surface 693
16.5.2 Mean Velocity in the Adiabatic Surface Layer over a Rough Surface 694
16.5.3 Mean Velocity Profiles in the Nonadiabatic Surface Layer 695
16.5.4 The Pasquill Stability Classes Estimation of L 698
16.5.5 Empirical Equation for the Mean Windspeed 700
Appendix 16.1 Properties of Water and Water Solutions 701
16A.1 Specific Heat of Water and Ice 701
16A.2 Latent Heats of Vaporization and Melting for Water 701
16A.3 Water Surface Tension 701
Appendix 16.2 Derivation of the Basic Equations of Surface–Layer Atmospheric Fluid Mechanics 702
Problems 705
References 706

Chapter 17 | Cloud Physics 708
17.1 Equilibrium of Water Droplets in the Atmosphere 708
17.1.1 Equilibrium of a Pure Water Droplet 708
17.1.2 Equilibrium of a Flat Water Solution 710
17.1.3 Atmospheric Equilibrium of an Aqueous Solution Drop 712
17.1.4 Atmospheric Equilibrium of an Aqueous Solution Drop Containing an Insoluble Substance 717
17.2 Cloud and Fog Formation 719
17.2.1 Isobaric Cooling 720
17.2.2 Adiabatic Cooling 720
17.2.3 A Simplified Mathematical Description of Cloud Formation 721
17.3 Growth Rate of Individual Cloud Droplets 723
17.4 Growth of a Droplet Population 726
17.5 Cloud Condensation Nuclei 730
17.5.1 Ambient CCN 733
17.5.2 The Hygroscopic Parameter Kappa 733
17.6 Cloud Processing of Aerosols 736
17.6.1 Nucleation Scavenging of Aerosols by Clouds 736
17.6.2 Chemical Composition of Cloud Droplets 737
17.6.3 Nonraining Cloud Effects on Aerosol Concentrations 739
17.6.4 Interstitial Aerosol Scavenging by Cloud Droplets 742
17.7 Other Forms of Water in the Atmosphere 743
17.7.1 Ice Clouds 743
17.7.2 Rain 747
Appendix 17 Extended Köhler Theory 751
17A.1 Modified Form of Köhler Theory for a Soluble Trace Gas 751
17A.2 Modified Form of Köhler Theory for a Slightly Soluble Substance 754
17A.3 Modified Form of Köhler Theory for a Surface–Active Solute 755
17A.4 Examples 756
Problems 759
References 760

Chapter 18 | Atmospheric Diffusion 763
18.1 Eulerian Approach 763
18.2 Lagrangian Approach 766
18.3 Comparison of Eulerian and Lagrangian Approaches 767
18.4 Equations Governing the Mean Concentration of Species in Turbulence 767
18.4.1 Eulerian Approaches 767
18.4.2 Lagrangian Approaches 769
18.5 Solution of the Atmospheric Diffusion Equation for an Instantaneous Source 771
18.6 Mean Concentration from Continuous Sources 772
18.6.1 Lagrangian Approach 772
18.6.2 Eulerian Approach 776
18.6.3 Summary of Continuous Point Source Solutions 777
18.7 Statistical Theory of Turbulent Diffusion 778
18.7.1 Qualitative Features of Atmospheric Diffusion 778
18.7.2 Motion of a Single Particle Relative to a Fixed Axis 780
18.8 Summary of Atmospheric Diffusion Theories 783
18.9 Analytical Solutions for Atmospheric Diffusion: the Gaussian Plume Equation and Others 784
18.9.1 Gaussian Concentration Distributions 784
18.9.2 Derivation of the Gaussian Plume Equation as a Solution of the Atmospheric Diffusion Equation 786
18.9.3 Summary of Gaussian Point Source Diffusion Formulas 791
18.10 Dispersion Parameters in Gaussian Models 791
18.10.1 Correlations for y and z Based on Similarity Theory 791
18.10.2 Correlations for y and z Based on Pasquill Stability Classes 795
18.11 Plume Rise 796
18.12 Functional Forms of Mean Windspeed and Eddy Diffusivities 798
18.12.1 Mean Windspeed 800
18.12.2 Vertical Eddy Diffusion Coefficient Kzz 800
18.12.3 Horizontal Eddy Diffusion Coefficients Kxx and Kyy 803
18.13 Solutions of the Steady–State Atmospheric Diffusion Equation 803
18.13.1 Diffusion from a Point Source 804
18.13.2 Diffusion from a Line Source 805
Appendix 18.1 Further Solutions of Atmospheric Diffusion Problems 807
18A.1 Solution of (18.29) (18.31) 807
18A.2 Solution of (18.50) and (18.51) 809
18A.3 Solution of (18.59) (18.61) 810
Appendix 18.2 Analytical Properties of the Gaussian Plume Equation 811
Problems 815
References 823

PART V | Dry and Wet Deposition

Chapter 19 | Dry Deposition 829
19.1 Deposition Velocity 829
19.2 Resistance Model for Dry Deposition 830
19.3 Aerodynamic Resistance 834
19.4 Quasilaminar Resistance 835
19.4.1 Gases 836
19.4.2 Particles 836
19.5 Surface Resistance 839
19.5.1 Surface Resistance for Dry Deposition of Gases to Water 841
19.5.2 Surface Resistance for Dry Deposition of Gases to Vegetation 845
19.6 Measurement of Dry Deposition 849
19.6.1 Direct Methods 849
19.6.2 Indirect Methods 850
19.6.3 Comparison of Methods 851
19.7 Some Comments on Modeling and Measurement of Dry Deposition 851
Problems 852
References 854

Chapter 20 | Wet Deposition 856
20.1 General Representation of Atmospheric Wet Removal Processes 856
20.2 Below–Cloud Scavenging of Gases 860
20.2.1 Below–Cloud Scavenging of an Irreversibly Soluble Gas 861
20.2.2 Below–Cloud Scavenging of a Reversibly Soluble Gas 864
20.3 Precipitation Scavenging of Particles 868
20.3.1 Raindrop Aerosol Collision Efficiency 870
20.3.2 Scavenging Rates 871
20.4 In–Cloud Scavenging 873
20.5 Acid Deposition 874
20.5.1 Acid Rain Overview 874
20.5.2 Surface Water Acidification 876
20.5.3 Cloudwater Deposition 877
20.5.4 Fogs and Wet Deposition 877
20.6 Acid Deposition Process Synthesis 878
20.6.1 Chemical Species Involved in Acid Deposition 878
20.6.2 Dry versus Wet Deposition 878
20.6.3 Chemical Pathways for Sulfate and Nitrate Production 878
20.6.4 Source Receptor Relationships 879
20.6.5 Linearity 880
Problems 881
References 886

PART VI | The Global Atmosphere, Biogeochemical Cycles, and Climate

Chapter 21 | General Circulation of the Atmosphere 891
21.1 Hadley Cell 893
21.2 Ferrell Cell and Polar Cell 893
21.3 Coriolis Force 895
21.4 Geostrophic Windspeed 897
21.4.1 Buys Ballot s Law 899
21.4.2 Ekman Spiral 900
21.5 The Thermal Wind Relation 902
21.6 Stratospheric Dynamics 905
21.7 The Hydrologic Cycle 905
Problems 906
References 907

Chapter 22 | Global Cycles: Sulfur and Carbon 908
22.1 The Atmospheric Sulfur Cycle 908
22.2 The Global Carbon Cycle 912
22.2.1 Carbon Dioxide 912
22.2.2 Compartmental Model of the Global Carbon Cycle 914
22.2.3 Atmospheric Lifetime of CO2 921
22.3 Solution for a Steady–State Four–Compartment Model of the Atmosphere 923
Problems 927
References 929

Chapter 23 | Global Climate 931
23.1 Earth s Energy Balance 931
23.2 Radiative Forcing 933
23.2.1 Climate Sensitivity 934
23.2.2 Climate Feedbacks 935
23.2.3 Timescales of Climate Change 935
23.3 The Greenhouse Effect 936
23.4 Climate–Forcing Agents 942
23.4.1 Solar Irradiance 942
23.4.2 Greenhouse Gases 945
23.4.3 Radiative Efficiencies of Greenhouse Gases 946
23.4.4 Aerosols 946
23.4.5 Summary of IPCC (2013) Estimated Forcing 947
23.4.6 The Preindustrial Atmosphere 948
23.5 Cosmic Rays and Climate 949
23.6 Climate Sensitivity 950
23.7 Simplified Dynamic Description of Climate Forcing and Response 951
23.7.1 Response to a Perturbation of Earth s Radiative Equilibrium 951
23.7.2 Physical Interpretation of Feedback Factors 954
23.8 Climate Feedbacks 955
23.8.1 Water Vapor Feedback 955
23.8.2 Lapse Rate Feedback 956
23.8.3 Cloud Feedback 956
23.8.4 Arctic Sea Ice Feedback 958
23.8.5 Summary of Feedbacks 958
23.9 Relative Radiative Forcing Indices 960
23.10 Atmospheric Chemistry and Climate Change 961
23.10.1 Indirect Chemical Impacts 962
23.10.2 Atmospheric Lifetimes and Adjustment Times 963
23.11 Conclusion 964
Problems 965
References 967

Chapter 24 | Aerosols and Climate 970
24.1 Scattering Absorbing Model of an Aerosol Layer 972
24.2 Cooling Versus Heating of an Aerosol Layer 975
24.3 Scattering Model of an Aerosol Layer for a Nonabsorbing Aerosol 977
24.4 Upscatter Fraction 979
24.5 Optical Depth and Column Forcing 981
24.6 Internal and External Mixtures 985
24.7 Top–of–the–Atmosphere Versus Surface Forcing 987
24.8 Indirect Effects of Aerosols on Climate 990
24.8.1 Stratocumulus Clouds 991
24.8.2 Simplified Model for Cloud Albedo 993
24.8.3 Albedo Susceptibility: Simplified Model 995
24.8.4 Albedo Susceptibility: Additional Considerations 997
24.8.5 A General Equation for Cloud Albedo Susceptibility 999
24.8.6 Estimating Indirect Aerosol Forcing on Climate 1003
Problems 1004
References 1004

PART VII | Chemical Transport Models and Statistical Models

Chapter 25 | Atmospheric Chemical Transport Models 1011
25.1 Introduction 1011
25.1.1 Model Types 1012
25.1.2 Types of Atmospheric Chemical Transport Models 1013
25.2 Box Models 1014
25.2.1 The Eulerian Box Model 1015
25.2.2 A Lagrangian Box Model 1017
25.3 Three–Dimensional Atmospheric Chemical Transport Models 1020
25.3.1 Coordinate System Uneven Terrain 1020
25.3.2 Initial Conditions 1022
25.3.3 Boundary Conditions 1023
25.4 One–Dimensional Lagrangian Models 1024
25.5 Other Forms of Chemical Transport Models 1026
25.5.1 Atmospheric Diffusion Equation Expressed in Terms of Mixing Ratio 1026
25.5.2 Pressure–Based Coordinate System 1029
25.5.3 Spherical Coordinates 1031
25.6 Numerical Solution of Chemical Transport Models 1031
25.6.1 Coupling Problem Operator Splitting 1032
25.6.2 Chemical Kinetics 1037
25.6.3 Diffusion 1041
25.6.4 Advection 1042
25.7 Model Evaluation 1046
25.8 Response of Organic and Inorganic Aerosols to Changes in Emission 1047
Problems 1048
References 1050

Chapter 26 | Statistical Models 1051
26.1 Receptor Modeling Methods 1051
26.2 Chemical Mass Balance (CMB) 1054
26.2.1 CMB Evaluation 1058
26.2.2 CMB Resolution 1059
26.2.3 CMB Codes 1059
26.3 Factor Analysis 1059
26.3.1 Principal–Component Analysis (PCA) 1061
26.3.2 Positive Matrix Factorization (PMF) 1064
26.4 Methods Incorporating Wind Information 1067
26.4.1 Potential Source Contribution Function (PSCF) 1068
26.4.2 Empirical Orthogonal Function (EOF) 1070
26.5 Probability Distributions for Air Pollutant Concentrations 1072
26A.1 The Lognormal Distribution 1073
26A.2 The Weibull Distribution 1074
26.6 Estimation of Parameters in the Distributions 1074
26A.1 Method of Quantiles 1075
26A.2 Method of Moments 1076
26.7 Order Statistics of Air Quality Data 1078
26A.1 Basic Notions and Terminology of Order Statistics 1078
26A.2 Extreme Values 1079
26.8 Exceedances of Critical Levels 1080
26.9 Alternative Forms of Air Quality Standards 1080
26.10 Relating Current and Future Air Pollutant Statistical Distributions 1083
Problems 1085
References 1087
Appendixes

Appendix A: | Units and Physical Constants 1091
A.1 SI Base Units 1091
A.2 SI Derived Units 1092
A.3 Fundamental Physical Constants 1094
A.4 Properties of the Atmosphere and Water 1094
A.5 Units for Representing Chemical Reactions 1096
A.6 Concentrations in the Aqueous Phase 1096
A.7 Symbols Denoting Concentration 1097
References 1097

Appendix B: | Rate Constants of Atmospheric Chemical Reactions 1098
References 1106

Appendix C: | Abbreviations 1107
Index 1112