Preface to the Second Edition ................................. vii
Preface to the First Edition ................................... ix
1. The Atmosphere .............................................. 1
1.1. History and Evolution of the Earth's Atmosphere ....... 1
1.2. Climate ............................................... 4
1.3. The Layers of the Atmosphere .......................... 6
1.4. Pressure in the Atmosphere ............................ 8
1.4.1. Units of Pressure ............................. 8
1.4.2. Variation of Pressure with Height in
the Atmosphere ................................ 9
1.5. Temperature in the Atmosphere ........................ 11
1.6. Expressing the Amount of a Substance in
the Atmosphere ....................................... 12
1.7. Spatial and Temporal Scales of Atmospheric
Processes ............................................ 16
Problems ................................................... 19
References ................................................. 20
2. Atmospheric Trace Constituents ............................. 22
2.1. Atmospheric Lifetime ................................. 22
2.2. Sulfur-Containing Compounds .......................... 27
2.2.1. Dimethyl Sulfide (CH3SCH3) ................... 31
2.2.2. Carbonyl Sulfide (OCS) ....................... 32
2.2.3. Sulfur Dioxide (S02) ......................... 33
2.3. Nitrogen-Containing Compounds ........................ 33
2.3.1. Nitrous Oxide (N20) .......................... 35
2.3.2. Nitrogen Oxides (NOx = NO + N02) ............. 36
2.3.3. Reactive Odd Nitrogen (NOy) .................. 37
2.3.4. Ammonia (NH3) ................................ 38
2.4. Carbon-Containing Compounds .......................... 38
2.4.1. Classification of Hydrocarbons ............... 38
2.4.2. Methane ...................................... 41
2.4.3. Volatile Organic Compounds ................... 43
2.4.4. Biogenic Hydrocarbons ........................ 43
2.4.5. Carbon Monoxide .............................. 46
2.4.6. Carbon Dioxide ............................... 47
2.5. Halogen-Containing Compounds ......................... 47
2.5.1. Methyl Chloride (CH3C1) ...................... 50
2.5.2. Methyl Bromide (CH3Br) ....................... 51
2.6. Atmospheric Ozone .................................... 52
2.7. Particulate Matter (Aerosols) ........................ 55
2.7.1. Stratospheric Aerosol ........................ 57
2.7.2. Chemical Components of Tropospheric
Aerosol ...................................... 57
2.7.3. Cloud Condensation Nuclei (CCN) .............. 58
2.7.4. Sizes of Atmospheric Particles ............... 58
2.7.5. Sources of Atmospheric Particulate Matter .... 60
2.7.6. Carbonaceous Particles ....................... 60
2.7.7. Mineral Dust ................................. 61
2.8. Emission Inventories ................................. 62
2.9. Biomass Burning ...................................... 63
Appendix 2.1. Air Pollution Legislation .................... 63
Appendix 2.2. Hazardous Air Pollutants (Air Toxics) ........ 65
Problems ................................................... 69
References ................................................. 70
3. Chemical Kinetics .......................................... 75
3.1. Order of Reaction .................................... 75
3.2. Theories of Chemical Kinetics ........................ 77
3.2.1. Collision Theory ............................. 77
3.2.2. Transition State Theory ...................... 80
3.2.3. Potential Energy Surface for a Bimolecular
Reaction ..................................... 82
3.3. The Pseudo-Steady-State Approximation ................ 83
3.4. Reactions of Excited Species ......................... 84
3.5. Termolecular Reactions ............................... 85
3.6. Chemical Families .................................... 89
3.7. Gas-Surface Reactions ................................ 91
Appendix 3. Free Radicals .................................. 93
Problems ................................................... 93
References ................................................. 96
4. Atmospheric Radiation and Photochemistry ................... 98
4.1. Radiation ............................................ 98
4.1.1. Solar and Terrestrial Radiation ............. 100
4.1.2. Energy Balance for Earth and Atmosphere ..... 101
4.1.3. Solar Variability ........................... 105
4.2. Radiative Flux in the Atmosphere .................... 106
4.3. Beer-Lambert Law and Optical Depth .................. 108
4.4. Actinic Flux ........................................ 111
4.5. Atmospheric Photochemistry .......................... 114
4.6. Absorption of Radiation by Atmospheric Gases ........ 117
4.7. Absorption by 02 and 03 ............................. 122
4.8. Photolysis Rate as a Function of Altitude ........... 126
4.9. Photodissociation of 03 to Produce O and O('D) ...... 128
4.10. Photodissociation of N02 ............................ 131
Problems .................................................. 135
References ................................................ 136
5. Chemistry of the Stratosphere ............................. 138
5.1. Overview of Stratospheric Chemistry ................. 138
5.2. Chapman Mechanism ................................... 142
5.3. Nitrogen Oxide Cycles ............................... 151
5.3.1. Stratospheric Source of NOx from N20 ........ 151
5.3.2. NOx Cycles .................................. 154
5.4. HOx Cycles .......................................... 156
5.5. Halogen Cycles ...................................... 162
5.5.1. Chlorine Cycles ............................. 162
5.5.2. Bromine Cycles .............................. 166
5.6. Reservoir Species and Coupling of the Cycles ........ 167
5.7. Ozone Hole .......................................... 169
5.7.1. Polar Stratospheric Clouds .................. 173
5.7.2. PSCs and the Ozone Hole ..................... 174
5.7.3. Arctic Ozone Hole ........................... 178
5.8. Heterogeneous (Nonpolar) Stratospheric Chemistry .... 179
5.8.1. The Stratospheric Aerosol Layer ............. 179
5.8.2. Heterogeneous Hydrolysis of N205 ............ 180
5.8.3. Effect of Volcanoes on Stratospheric
Ozone ....................................... 185
5.9. Summary of Stratospheric Ozone Depletion ............ 188
5.10. Transport and Mixing in the Stratosphere ............ 191
5.11. Ozone Depletion Potential ........................... 193
Problems .................................................. 195
References ................................................ 200
6. Chemistry of the Troposphere .............................. 204
6.1. Production of Hydroxyl Radicals in the
Troposphere ......................................... 205
6.2. Basic Photochemical Cycle of N02, NO, and 03 ........ 209
6.3. Atmospheric Chemistry of Carbon Monoxide ............ 211
6.3.1. Low NOx Limit ............................... 214
6.3.2. High NOx Limit .............................. 214
6.3.3. Ozone Production Efficiency ................. 215
6.3.4. Theoretical Maximum Yield of Ozone from
CO Oxidation ................................ 219
6.4. Atmospheric Chemistry of Methane .................... 219
6.5. The NOx and NOy Families ............................ 224
6.5.1. Daytime Behavior ............................ 224
6.5.2. Nighttime Behavior .......................... 225
6.6. Ozone Budget of the Troposphere and Role of NOx ..... 227
6.6.1. Ozone Budget of the Troposphere ............. 227
6.6.2. Role of NOx ................................. 228
6.7. Tropospheric Reservoir Molecules .................... 231
6.7.1. H202, CH3OOH, and HONO ...................... 231
6.7.2. Peroxyacyl Nitrates (PANs) .................. 231
6.8. Relative Roles of VOC and NOx in Ozone Formation .... 235
6.8.1. Importance of the VOC/NOx Ratio ............. 235
6.8.2. Ozone Isopleth Plot ......................... 236
6.9. Simplified Organic/NOx Chemistry .................... 239
6.10. Chemistry of Nonmethane Organic Compounds in the
Troposphere ......................................... 242
6.10.1. Alkanes ..................................... 242
6.10.2. Alkenes ..................................... 247
6.10.3. Aromatics ................................... 254
6.10.4. Aldehydes ................................... 258
6.10.5. Ketones ..................................... 259
6.10.6. α, β-Unsaturated Carbonyls .................. 260
6.10.7. Ethers ...................................... 260
6.10.8. Alcohols .................................... 261
6.11. Atmospheric Chemistry of Biogenic Hydrocarbons ...... 261
6.12. Atmospheric Chemistry of Reduced Nitrogen
Compounds ........................................... 265
6.12.1. Amines ...................................... 265
6.12.2. Nitriles .................................... 266
6.12.3. Nitrites .................................... 266
6.13. Atmospheric Chemistry (Gas Phase) of Sulfur
Compounds ........................................... 266
6.13.1. Sulfur Oxides ............................... 266
6.13.2. Reduced Sulfur Compounds
(Dimethyl Sulfide) .......................... 267
6.14. Tropospheric Chemistry of Halogen Compounds ......... 270
6.14.1. Chemical Cycles of Halogen Species .......... 270
6.14.2. Tropospheric Chemistry of CFC
Replacements: Hydrofiuorocarbons (HFCs)
and Hydrochlorofluorocarbons (HCFCs) ........ 272
Problems .................................................. 275
References ................................................ 279
7. Chemistry of the Atmospheric Aqueous Phase ................ 284
7.1. Liquid Water in the Atmosphere ...................... 284
7.2. Absorption Equilibria and Henry's Law ............... 286
7.3. Aqueous-Phase Chemical Equilibria ................... 291
7.3.1. Water ....................................... 291
7.3.2. Carbon Dioxide-Water Equilibrium ............ 292
7.3.3. Sulfur Dioxide-Water Equilibrium ............ 294
7.3.4. Ammonia-Water Equilibrium ................... 299
7.3.5. Nitric Acid-Water Equilibrium ............... 299
7.3.6. Equilibria of Other Important Atmospheric
Gases ....................................... 302
7.4. Aqueous-Phase Reaction Rates ........................ 306
7.5. S(IV)-S(VI) Transformation and Sulfur Chemistry ..... 308
7.5.1. Oxidation of S(IV) by Dissolved 03 .......... 308
7.5.2. Oxidation of S(IV) by Hydrogen Peroxide ..... 311
7.5.3. Oxidation of S(IV) by Organic Peroxides ..... 312
7.5.4. Uncatalyzed Oxidation of S(IV) by 02 ........ 313
7.5.5. Oxidation of S(IV) by 02 Catalyzed by Iron
and Manganese ............................... 314
7.5.6. Comparison of Aqueous-Phase S(IV)
Oxidation Paths ............................. 316
7.6. Dynamic Behavior of Solutions with Aqueous-Phase
Chemical Reactions .................................. 318
7.6.1. Closed System ............................... 319
7.6.2. Calculation of Concentration Changes in a
Droplet with Aqueous-Phase Reactions ........ 321
Appendix 7.1. Thermodynamic and Kinetic Data .............. 325
Appendix 7.2. Additional Aqueous-Phase Sulfur Chemistry ... 328
7.A.1. S(IV) Oxidation by the OH Radical ........... 328
7.A.2. Oxidation of S(IV) by Oxides of Nitrogen .... 334
7.A.3. Reaction of Dissolved S02 with HCHO ......... 334
Appendix 7.3. Aqueous-Phase Nitrite and Nitrate
Chemistry ................................... 336
7.A.4. NOx Oxidation ............................... 336
7.A.5. Nitrogen Radicals 337
Appendix 7.4. Aqueous-Phase Organic Chemistry ............. 338
Appendix 7.5. Oxygen and Hydrogen Chemistry ............... 339
Problems .................................................. 340
References ................................................ 343
8. Properties of the Atmospheric Aerosol ..................... 350
8.1. The Size Distribution Function ...................... 350
8.1.1. The Number Distribution nN(Dp) .............. 353
8.1.2. The Surface Area, Volume, and Mass
Distributions ............................... 355
8.1.3. Distributions Based on ln Dp and log Dp ..... 358
8.1.4. Relating Size Distributions Based on
Different Independent Variables ............. 359
8.1.5. Properties of Size Distributions ............ 360
8.1.6. The Lognormal Distribution .................. 362
8.1.7. Plotting the Lognormal Distribution ......... 365
8.1.8. Properties of the Lognormal Distribution .... 366
8.2. Ambient Aerosol Size Distributions .................. 368
8.2.1. Urban Aerosols .............................. 370
8.2.2. Marine Aerosols ............................. 374
8.2.3. Rural Continental Aerosols .................. 375
8.2.4. Remote Continental Aerosols ................. 376
8.2.5. Free Tropospheric Aerosols .................. 376
8.2.6. Polar Aerosols .............................. 378
8.2.7. Desert Aerosols ............................. 379
8.3. Aerosol Chemical Composition ........................ 381
8.4. Spatial and Temporal Variation ...................... 384
8.5. Vertical Variation .................................. 388
Problems .................................................. 389
References ................................................ 393
9. Dynamics of Single Aerosol Particles ...................... 396
9.1. Continuum and Noncontinuum Dynamics: The Mean Free
Path ................................................ 396
9.2. The Drag on a Single Particle: Stokes' Law .......... 403
9.2.1. Corrections to Stokes' Law: The Drag
Coefficient ................................. 405
9.2.2. Stokes' Law and Noncontinuum Effects: Slip
Correction Factor ........................... 406
9.3. Gravitational Settling of an Aerosol Particle ....... 407
9.4. Motion of an Aerosol Particle in an External Force
Field ............................................... 411
9.5. Brownian Motion of Aerosol Particles ................ 412
9.5.1. Particle Diffusion .......................... 415
9.5.2. Aerosol Mobility and Drift Velocity ......... 417
9.5.3. Mean Free Path of an Aerosol Particle ....... 420
9.6. Aerosol and Fluid Motion ............................ 422
9.6.1. Motion of a Particle in an Idealized Flow
(90° Corner) ................................ 423
9.6.2. Stop Distance and Stokes Number ............. 425
9.7. Equivalent Particle Diameters ....................... 426
9.7.1. Volume Equivalent Diameter .................. 426
9.7.2. Stokes Diameter ............................. 428
9.7.3. Classical Aerodynamic Diameter .............. 429
9.7.4. Electrical Mobility Equivalent Diameter ..... 431
Problems .................................................. 431
References ................................................ 432
10. Thermodynamics of Aerosols ................................ 434
10.1. Thermodynamic Principles ............................ 434
10.1.1. Internal Energy and Chemical Potential ...... 434
10.1.2. The Gibbs Free Energy, G .................... 436
10.1.3. Conditions for Chemical Equilibrium ......... 438
10.1.4. Chemical Potentials of Ideal Gases and
Ideal-Gas Mixtures .......................... 442
10.1.5. Chemical Potential of Solutions ............. 443
10.1.6. The Equilibrium Constant .................... 448
10.2. Aerosol Liquid Water Content ........................ 449
10.2.1. Chemical Potential of Water in Atmospheric
Particles ................................... 452
10.2.2. Temperature Dependence of the DRH ........... 453
10.2.3. Deliquescence of Multicomponent Aerosols .... 455
10.2.4. Crystallization of Single and
Multicomponent Salts ........................ 460
10.3. Equilibrium Vapor Pressure over a Curved Surface:
the Kelvin Effect ................................... 461
10.4. Thermodynamics of Atmospheric Aerosol Systems ....... 464
10.4.1. The H2S04-H20 System ........................ 464
10.4.2. The Sulfuric Acid-Ammonia-Water System ...... 470
10.4.3. The Ammonia-Nitric Acid-Water System ........ 472
10.4.4. The Ammonia - Nitric Acid - Sulfuric
Acid - Water System ......................... 478
10.4.5. Other Inorganic Aerosol Species ............. 483
10.4.6. Inorganic Aerosol Thermodynamic Models ...... 484
Problems .................................................. 485
References ................................................ 486
11. Nucleation ................................................ 489
11.1. Classical Theory of Homogeneous Nucleation:
Kinetic Approach .................................... 491
11.1.1. The Forward Rate Constant βi ................ 494
11.1.2. The Reverse Rate Constant γi ................ 495
11.1.3. Derivation of the Nucleation Rate ........... 496
11.2. Classical Homogeneous Nucleation Theory:
Constrained Equilibrium Approach .................... 500
11.2.1. Free Energy of i-mer Formation .............. 500
11.2.2. Constrained Equilibrium Cluster
Distribution ................................ 502
11.2.3. The Evaporation Coefficient γi .............. 504
11.2.4. Nucleation Rate ............................. 505
11.3. Recapitulation of Classical Theory .................. 508
11.4. Experimental Measurement of Nucleation Rates ........ 509
11.4.1. Upward Thermal Diffusion Cloud Chamber ...... 510
11.4.2. Fast Expansion Chamber ...................... 510
11.4.3. Turbulent Mixing Chambers ................... 512
11.4.4. Experimental Evaluation of Classical
Homogeneous Nucleation Theory ............... 512
11.5. Modifications of the Classical Theory and More
Rigorous Approaches ................................. 513
11.6. Binary Homogeneous Nucleation ....................... 514
11.7. Binary Nucleation in the H2S04-H20 System ........... 520
11.8. Heterogeneous Nucleation ............................ 524
11.8.1. Nucleation on an Insoluble Foreign
Surface ..................................... 524
11.8.2. Ion-Induced Nucleation ...................... 526
11.9. Nucleation in the Atmosphere ........................ 529
Appendix 11. The Law of Mass Action ...................... 531
Problems .................................................. 532
References ................................................ 533
12. Mass Transfer Aspects of Atmospheric Chemistry ............ 537
12.1. Mass and Heat Transfer to Atmospheric Particles ..... 537
12.1.1. The Continuum Regime ........................ 537
12.1.2. The Kinetic Regime .......................... 541
12.1.3. The Transition Regime ....................... 542
12.1.4. The Accommodation Coefficient ............... 546
12.2. Mass Transport Limitations in Aqueous-Phase
Chemistry ........................................... 547
12.2.1. Characteristic Time for Gas-Phase
Diffusion to a Particle ..................... 549
12.2.2. Characteristic Time to Achieve Equilibrium
in the Gas-Particle Interface ............... 551
12.2.3. Characteristic Time of Aqueous
Dissociation Reactions ...................... 554
12.2.4. Characteristic Time of Aqueous-Phase
Diffusion in a Droplet ...................... 556
12.2.5. Characteristic Time for Aqueous-Phase
Chemical Reactions .......................... 557
12.3. Mass Transport and Aqueous-Phase Chemistry .......... 557
12.3.1. Gas-Phase Diffusion and Aqueous-Phase
Reactions ................................... 558
12.3.2. Aqueous-Phase Diffusion and Reaction ........ 560
12.3.3. Interfacial Mass Transport and Aqueous-
Phase Reactions ............................. 561
12.3.4. Application to the S(IV)-Ozone Reaction ..... 564
12.3.5. Application to the S(IV)-Hydrogen Peroxide
Reaction .................................... 566
12.3.6. Calculation of Aqueous-Phase Reaction
Rates ....................................... 567
12.3.7. An Aqueous-Phase Chemistry/Mass Transport
Model ....................................... 573
12.4. Mass Transfer to Falling Drops ...................... 574
12.5. Characteristic Time for Atmospheric Aerosol
Equilibrium ......................................... 575
12.5.1. Solid Aerosol Particles ..................... 575
12.5.2. Aqueous Aerosol Particles ................... 577
Appendix 12. Solution of the Transient Gas-Phase
Diffusion Problem Equations (12.4)-(12.7) ... 580
Problems .................................................. 582
References ................................................ 584
13. Dynamics of Aerosol Populations ........................... 588
13.1. Mathematical Representations of Aerosol Size
Distributions ....................................... 588
13.1.1. Discrete Distribution ....................... 588
13.1.2. Continuous Distribution ..................... 589
13.2. Condensation ........................................ 589
13.2.1. The Condensation Equation ................... 589
13.2.2. Solution of the Condensation Equation ....... 592
13.3. Coagulation ......................................... 595
13.3.1. Brownian Coagulation ........................ 596
13.3.2. The Coagulation Equation .................... 603
13.3.3. Solution of the Coagulation Equation ........ 606
13.4. The Discrete General Dynamic Equation ............... 610
13.5. The Continuous General Dynamic Equation ............. 612
Appendix 13.1.Additional Mechanisms of Coagulation ........ 613
13.A.1. Coagulation in Laminar Shear Flow ........... 613
13.A.2. Coagulation in Turbulent Flow ............... 614
13.A.3. Coagulation from Gravitational Settling ..... 614
13.A.4. Brownian Coagulation and External Force
Fields ...................................... 615
Appendix 13.2.Solution of (13.73) ......................... 620
Problems .................................................. 622
References ................................................ 626
14. Organic Atmospheric Aerosols .............................. 628
14.1. Organic Aerosol Components .......................... 628
14.2. Elemental Carbon .................................... 628
14.2.1. Formation of Soot and Elemental Carbon ...... 628
14.2.2. Emission Sources of Elemental Carbon ........ 630
14.2.3. Ambient Elemental Carbon Concentrations ..... 632
14.2.4. Ambient Elemental Carbon Size
Distribution ................................ 633
14.3. Organic Carbon ...................................... 634
14.3.1. Ambient Aerosol Organic Carbon
Concentrations .............................. 635
14.3.2. Primary versus Secondary Organic Carbon ..... 636
14.4. Primary Organic Carbon .............................. 640
14.4.1. Sources ..................................... 640
14.4.2. Chemical Composition ........................ 642
14.4.3. Primary ОС Size Distribution ................ 645
14.5. Secondary Organic Carbon ............................ 647
14.5.1. Overview of Secondary Organic Aerosol
Formation Pathways .......................... 647
14.5.2. Dissolution and Gas-Particle Partitioning
of Organic Compounds ........................ 650
14.5.3. Adsorption and Gas-Particle Partitioning
of Organic Compounds ........................ 658
14.5.4. Precursor Volatile Organic Compounds ........ 661
14.5.5. SOA Yields .................................. 664
14.5.6. Chemical Composition ........................ 665
14.5.7. Physical Properties of SOA Components ....... 666
14.5.8. Particle-Phase Chemistry .................... 666
14.6. Polycyclic Aromatic Hydrocarbons (PAHs) ............. 670
14.6.1. Emission Sources ............................ 671
14.6.2. Size Distributions .......................... 671
14.6.3. Atmospheric Chemistry ....................... 671
14.6.4. Partitioning between Gas and Aerosol
Phases ...................................... 672
Appendix 14. Measurement of Elemental and Organic
Carbon ...................................... 675
Problems .................................................. 677
References ................................................ 678
15. Interaction of Aerosols with Radiation .................... 691
15.1. Scattering and Absorption of Light by Small
Particles ........................................... 691
15.1.1. Rayleigh Scattering Regime .................. 696
15.1.2. Geometric Scattering Regime ................. 698
15.1.3. Scattering Phase Function ................... 700
15.1.4. Extinction by an Ensemble of Particles ...... 700
15.2. Visibility .......................................... 703
15.3. Scattering, Absorption, and Extinction
Coefficients from Mie Theory ........................ 707
15.4. Calculated Visibility Reduction Based on
Atmospheric Data .................................... 711
Appendix 15. Calculation of Scattering and Extinction
Coefficients by Mie Theory .................. 715
Problems .................................................. 716
References ................................................ 718
16. Meteorology of the Local Scale ............................ 720
16.1. Temperature in the Lower Atmosphere ................. 722
16.1.1. Temperature Variation in a Neutral
Atmosphere .................................. 722
16.1.2. Potential Temperature ....................... 726
16.1.3. Buoyancy of a Rising (or Falling) Air
Parcel in the Atmosphere .................... 727
16.2. Atmospheric Stability ............................... 729
16.3. Micrometeorology .................................... 732
16.3.1. Basic Equations of Atmospheric Fluid
Mechanics ................................... 733
16.3.2. Turbulence .................................. 736
16.3.3. Equations for the Mean Quantities ........... 737
16.3.4. Mixing-Length Models for Turbulent
Transport ................................... 739
16.4. Variation of Wind with Height in the Atmosphere ..... 742
16.4.1. Mean Velocity in the Adiabatic Surface
Layer over a Smooth Surface ................. 743
16.4.2. Mean Velocity in the Adiabatic Surface
Layer over a Rough Surface .................. 744
16.4.3. Mean Velocity Profiles in the Nonadiabatic
Surface Layer ............................... 746
16.4.4. The Pasquill Stability Classes—Estimation
of L ........................................ 749
16.4.5. Empirical Equation for the Mean Wind
Speed ....................................... 752
Appendix 16. Derivation of the Basic Equations of
Surface Layer Atmospheric Fluid Mechanics ... 752
Problems................................................... 756
References ................................................ 759
17. Cloud Physics ............................................. 761
17.1. Properties of Water and Water Solutions ............. 761
17.1.1. Specific Heat of Water and Ice .............. 762
17.1.2. Latent Heats of Evaporation and of Melting
for Water ................................... 762
17.1.3. Water Surface Tension ....................... 762
17.2. Water Equilibrium in the Atmosphere ................. 763
17.2.1. Equilibrium of a Flat Pure Water Surface
with the Atmosphere ......................... 764
17.2.2. Equilibrium of a Pure Water Droplet ......... 765
17.2.3. Equilibrium of a Flat Water Solution ........ 766
17.2.4. Atmospheric Equilibrium of an Aqueous
Solution Drop ............................... 767
17.2.5. Atmospheric Equilibrium of an Aqueous
Solution Drop Containing an Insoluble
Substance ................................... 773
17.3. Cloud and Fog Formation ............................. 777
17.3.1. Isobaric Cooling ............................ 777
17.3.2. Adiabatic Cooling ........................... 778
17.3.3. Cooling with Entrainment .................... 780
17.3.4. A Simplified Mathematical Description of
Cloud Formation ............................. 781
17.4. Growth Rate of Individual Cloud Droplets ............ 783
17.5. Growth of a Droplet Population ...................... 786
17.6. Cloud Condensation Nuclei ........................... 791
17.7. Cloud Processing of Aerosols ........................ 794
17.7.1. Nucleation Scavenging of Aerosols by
Clouds ...................................... 794
17.7.2. Chemical Composition of Cloud Droplets ...... 795
17.7.3. Nonraining Cloud Effects on Aerosol
Concentrations .............................. 797
17.7.4. Interstitial Aerosol Scavenging by Cloud
Droplets .................................... 803
17.7.5. Aerosol Nucleation Near Clouds .............. 804
17.8. Other Forms of Water in the Atmosphere .............. 805
17.8.1. Ice Clouds .................................. 805
17.8.2. Rain ........................................ 809
Appendix 17. Extended Kohler Theory ...................... 812
17.A.1. Modified Form of Kohler Theory for a
Soluble Trace Gas ........................... 813
17.A.2. Modified Form of the Kohler Theory for a
Slightly Soluble Substance .................. 816
17.A.3. Modified Form of the Kohler Theory for
a Surface-Active Solute ..................... 818
17.A.4. Examples .................................... 818
Problems .................................................. 822
References ................................................ 823
18. Atmospheric Diffusion ..................................... 828
18.1. Eulerian Approach ................................... 828
18.2. Lagrangian Approach ................................. 831
18.3. Comparison of Eulerian and Lagrangian Approaches .... 832
18.4. Equations Governing the Mean Concentration of
Species in Turbulence ............................... 833
18.4.1. Eulerian Approaches ......................... 833
18.4.2. Lagrangian Approaches ....................... 834
18.5. Solution of the Atmospheric Diffusion Equation for
an Instantaneous Source ............................. 837
18.6. Mean Concentration from Continuous Sources .......... 838
18.6.1. Lagrangian Approach ......................... 838
18.6.2. Eulerian Approach ........................... 843
18.6.3. Summary of Continuous Point Source
Solutions ................................... 844
18.7. Statistical Theory of Turbulent Diffusion ........... 845
18.7.1. Qualitative Features of Atmospheric
Diffusion ................................... 845
18.7.2. Motion of a Single Particle Relative to
a Fixed Axis ................................ 847
18.8. Summary of Atmospheric Diffusion Theories ........... 851
18.9. Analytical Solutions for Atmospheric Diffusion:
The Gaussian Plume Equation and Others .............. 852
18.9.1. Gaussian Concentration Distributions ........ 852
18.9.2. Derivation of the Gaussian Plume Equation
as a Solution of the Atmospheric Diffusion
Equation .................................... 854
18.9.3. Summary of Gaussian Point Source Diffusion
Formulas .................................... 859
18.10.Dispersion Parameters in Gaussian Models ............ 859
18.10.1.Correlations for σy and σz Based on
Similarity Theory ........................... 862
18.10.2.Correlations for σy and σz Based on
Pasquill Stability Classes .................. 864
18.11.Plume Rise .......................................... 867
18.12.Functional Forms of Mean Windspeed and Eddy
Diffusivities ....................................... 869
18.12.1.Mean Windspeed .............................. 869
18.12.2.Vertical Eddy Diffusion Coefficient
Kzz ......................................... 869
18.12.3.Horizontal Eddy Diffusion Coefficients
Kxx and Kyy ................................. 873
18.13.Solutions of the Steady-State Atmospheric
Diffusion Equation .................................. 873
18.13.1.Diffusion from a Point Source ............... 874
18.13.2.Diffusion from a Line Source ................ 875
Appendix 18.1.Further Solutions of Atmospheric Diffusion
Problems .................................... 878
18.A.1. Solution of (18.29)-( 18.31) ................ 878
18.A.2. Solution of (18.50) and (18.51) ............. 880
18.A.3. Solution of (18.59)-(18.61) ................. 881
Appendix 18.2.Analytical Properties of the Gaussian Plume
Equation .................................... 882
Problems .................................................. 886
References ................................................ 896
19. Dry Deposition ............................................ 900
19.1. Deposition Velocity ................................. 900
19.2. Resistance Model for Dry Deposition ................. 902
19.3. Aerodynamic Resistance .............................. 906
19.4. Quasi-Laminar Resistance ............................ 907
19.4.1. Gases ....................................... 908
19.4.2. Particles ................................... 908
19.5. Surface Resistance .................................. 911
19.5.1. Surface Resistance for Dry Deposition
of Gases to Water ........................... 914
19.5.2. Surface Resistance for Dry Deposition of
Gases to Vegetation ......................... 918
19.6. Measurement of Dry Deposition ....................... 923
19.6.1. Direct Methods .............................. 923
19.6.2. Indirect Methods ............................ 925
19.6.3. Comparison of Methods ....................... 925
19.7. Some Comments on Modeling and Measurement
of Dry Deposition ................................... 926
Problems .................................................. 927
References ................................................ 929
20. Wet Deposition ............................................ 932
20.1. General Representation of Atmospheric Wet Removal
Processes ........................................... 932
20.2. Below-Cloud Scavenging of Gases ..................... 937
20.2.1. Below-Cloud Scavenging of an Irreversibly
Soluble Gas ................................. 938
20.2.2. Below-Cloud Scavenging of a Reversibly
Soluble Gas ................................. 942
20.3. Precipitation Scavenging of Particles ............... 947
20.3.1. Raindrop-Aerosol Collision Efficiency ....... 949
20.3.2. Scavenging Rates ............................ 951
20.4. In-Cloud Scavenging ................................. 953
20.5. Acid Deposition ..................................... 954
20.5.1. Acid Rain Overview .......................... 954
20.5.2. Acid Rain Data and Trends ................... 957
20.5.3. Effects of Acid Deposition .................. 959
20.5.4. Cloudwater Deposition ....................... 963
20.5.5. Fogs and Wet Deposition ..................... 964
20.6. Acid Deposition Process Synthesis ................... 965
20.6.1. Chemical Species Involved in Acid
Deposition .................................. 965
20.6.2. Dry versus Wet Deposition ................... 965
20.6.3. Chemical Pathways for Sulfate and Nitrate
Production .................................. 966
20.6.4. Source-Receptor Relationships ............... 968
20.6.5. Linearity ................................... 969
Problems .................................................. 971
References ................................................ 977
21. General Circulation of the Atmosphere ..................... 980
21.1. Hadley Cell ......................................... 981
21.2. Ferrell Cell and Polar Cell ......................... 983
21.3. Coriolis Force ...................................... 985
21.4. Geostrophic Windspeed ............................... 987
21.4.1. Buys Ballot's Law ........................... 989
21.4.2. Ekman Spiral ................................ 990
21.5. The Thermal Wind Relation ........................... 993
21.6. Stratospheric Dynamics .............................. 996
21.7. The Hydrologic Cycle ................................ 997
Appendix 21. Ocean Circulation ........................... 998
Problems ................................................. 1000
References ............................................... 1002
22. Global Cycles: Sulfur and Carbon ......................... 1003
22.1. The Atmospheric Sulfur Cycle ....................... 1003
22.2. The Global Carbon Cycle ............................ 1007
22.2.1. Carbon Dioxide ............................. 1007
22.2.2. Compartmental Model of the Global Carbon
Cycle ...................................... 1009
22.2.3. Atmospheric Lifetime of C02 ................ 1014
22.3. Analytical Solution for a Steady-State Four-
Compartment Model of the Atmosphere ................ 1018
Problems ................................................. 1023
References ............................................... 1024
23. Climate and Chemical Composition of the Atmosphere ....... 1026
23.1. The Global Temperature Record ...................... 1028
23.2. Solar Variability .................................. 1032
23.3. Radiative Forcing .................................. 1035
23.4. Climate Sensitivity ................................ 1039
23.5. Relative Radiative Forcing Indices ................. 1042
23.6. Unrealized Warming ................................. 1045
23.7. Atmospheric Chemistry and Climate Change ........... 1045
23.7.1. Indirect Chemical Impacts .................. 1046
23.7.2. Atmospheric Lifetimes and Adjustment
Times ...................................... 1048
23.8. Radiative Effects of Clouds ........................ 1049
Problems ................................................. 1049
References ............................................... 1052
24. Aerosols and Climate ..................................... 1054
24.1. Scattering-Absorbing Model of an Aerosol Layer ..... 1057
24.2. Cooling versus Heating of an Aerosol Layer ......... 1060
24.3. Scattering Model of an Aerosol Layer for
a Nonabsorbing Aerosol ............................. 1062
24.4. Upscatter Fraction ................................. 1064
24.5. Optical Depth and Column Forcing ................... 1067
24.6. Internal and External Mixtures ..................... 1071
24.7. Top-of-the-Atmosphere versus Surface Forcing ....... 1074
24.8. Indirect Effects of Aerosols on Climate ............ 1078
24.8.1. Radiative Model for a Cloudy Atmosphere .... 1080
24.8.2. Sensitivity of Cloud Albedo to Cloud
Droplet Number Concentration ............... 1082
24.8.3. Relation of Cloud Droplet Number
Concentration to Aerosol Concentrations .... 1084
Problems ................................................. 1087
References ............................................... 1088
25. Atmospheric Chemical Transport Models .................... 1092
25.1. Introduction ....................................... 1092
25.1.1. Model Types ................................ 1093
25.1.2. Types of Atmospheric Chemical Transport
Models ..................................... 1094
25.2. Box Models ......................................... 1096
25.2.1. The Eulerian Box Model ..................... 1096
25.2.2. A Lagrangian Box Model ..................... 1099
25.3. Three-Dimensional Atmospheric Chemical Transport
Models ............................................. 1102
25.3.1. Coordinate System—Uneven Terrain ........... 1102
25.3.2. Initial Conditions ......................... 1104
25.3.3. Boundary Conditions ........................ 1105
25.4. One-Dimensional Lagrangian Models .................. 1106
25.5. Other Forms of Chemical Transport Models ........... 1109
25.5.1. Atmospheric Diffusion Equation Expressed
in Terms of Mixing Ratio ................... 1109
25.5.2. Pressure-Based Coordinate System ........... 1113
25.5.3. Spherical Coordinates ...................... 1114
25.6. Numerical Solution of Chemical Transport Models .... 1115
25.6.1. Coupling Problem—Operator Splitting ........ 1116
25.6.2. Chemical Kinetics .......................... 1121
25.6.3. Diffusion .................................. 1126
25.6.4. Advection .................................. 1127
25.7. Model Evaluation ................................... 1131
Problems ................................................. 1133
References ............................................... 1135
26. Statistical Models ....................................... 1136
26.1. Receptor Modeling Methods .......................... 1136
26.1.1. Chemical Mass Balance (CMB) ................ 1139
26.1.2. Factor Analysis ............................ 1146
26.1.3. Empirical Orthogonal Function Receptor
Models ..................................... 1150
26.2. Probability Distributions for Air Pollutant
Concentrations ..................................... 1153
26.2.1. The Lognormal Distribution ................. 1154
26.2.2. The Weibull Distribution ................... 1154
26.3. Estimation of Parameters in the Distributions ...... 1156
26.3.1. Method of Quantiles ........................ 1157
26.3.2. Method of Moments .......................... 1157
26.4. Order Statistics of Air Quality Data ............... 1160
26.4.1. Basic Notions and Terminology of Order
Statistics ................................. 1160
26.4.2. Extreme Values ............................ 1161
26.5. Exceedances of Critical Levels ..................... 1162
26.6. Alternative Forms of Air Quality Standards ......... 1162
26.7. Relating Current and Future Air Pollutant
Statistical Distributions .......................... 1167
Problems ................................................. 1169
References ............................................... 1172
Appendix A.Units and Physical Constants .................. 1175
A.l. SI Base Units ................................. 1175
A.2. SI Derived Units .............................. 1175
A.3. Fundamental Physical Constants ................ 1178
A.4. Properties of the Atmosphere and Water ........ 1178
A.5. Units for Representing Chemical Reactions ..... 1180
A.6. Concentrations in the Aqueous Phase ........... 1180
A.7. Symbols for Concentration ..................... 1181
References ......................................... 1181
Appendix В.Rate Constants of Atmospheric Chemical
Reactions ..................................... 1182
References ......................................... 1190
Index ........................................................ 1191
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