Microphysics of Clouds and Precipitation (eBook)

TABLE OF CONTENTS 6
PREFACE TO THE FIRST EDITION 15
PREFACE TO THE SECOND EDITION 17
CHAPTER 1 HISTORICAL REVIEW 22
CHAPTER 2 MICROSTRUCTURE OF ATMOSPHERIC CLOUDS ANDPRECIPITATION 31
2.1 Microstructure of Clouds and Precipitation Consisting ofWater Drops 31
2.1.1 THE RELATIVE HUMIDITY INSIDE CLOUDS AND FOGS 31
2.1.2 MICROSTRUCTURE OF FOGS 33
2.1.3 MICROSTRUCTURE OF CLOUDS 36
2.1.4 FORMULATIONS FOR THE DROP SIZE DISTRIBUTIONS IN CLOUDSAND FOGS 45
2.1.5 THE MEAN DISTANCE BETWEEN DROPS IN CLOUDS AND FOGS 48
2.1.6 MICROSTRUCTURE OF RAIN 51
2.2 Microstructure of Clouds and Precipitation Consisting ofIce Particles 59
2.2.1 SHAPE, DIMENSIONS, BULK DENSITY AND NUMBER CONCENTRATIONOF SNOW CRYSTALS 61
2.2.2 SHAPE, DIMENSIONS, BULK DENSITY, AND NUMBER CONCENTRATIONOF SNOWFLAKES, GRAUPEL, AND HAILSTONES 79
CHAPTER 3 THE STRUCTURE OF WATER SUBSTANCE 95
3.1 Structure of an Isolated Water Molecule 95
3.2 Structure of Water Vapor 98
3.3 Structure of Ice 99
3.4 Structure of Water and Aqueous Solutions 107
3.4.1 STRUCTURE OF WATER 107
3.4.2 STRUCTURE OF AQUEOUS SOLUTIONS 119
CHAPTER 4 EQUILIBRIUM BETWEEN WATER VAPOR, WATER, AQUEOUSSOLUTIONS, AND ICE IN BULK 121
4.1 Useful Thermodynamic Relations 121
4.2 General Conditions for Equilibrium 123
4.3 Phase Rule for Bulk Phases 125
4.4 Ideal versus Real Behavior of Dry Air, Water Vapor, andMoist Air 126
4.5 Chemical Potential of Water Vapor in Humid Air, and ofWater in Aqueous Solutions 128
4.6 Equilibrium Between an Aqueous Salt Solution andWater Vapor 130
4.7 Latent Heat of Phase Change and its TemperatureVariation 136
4.8 Clausius-Clapeyron Equation 137
4.9 Equilibrium Between an Aqueous Salt Solution and Ice 144
CHAPTER 5 SURFACE PROPERTIES OF WATER SUBSTANCE 147
5.1 Surface Tension 147
5.2 Equilibrium Conditions 148
5.3 Phase Rule for Systems with Curved Interfaces 149
5.4 Water-Vapor Interface 150
5.4.1 EFFECT OF TEMPERATURE ON THE SURFACE TENSION OF WATER 151
5.4.2 SURFACE TENSION OF AQUEOUS SALT SOLUTIONS 151
5.5 Angle of Contact 156
5.6 Adsorption of Water Vapor on Solid Surfaces 158
5.7 Ice-Vapor Interface 166
5.7.1 SURFACE ENERGY OF ICE 166
5.7.2 WULFF'S THEOREM 168
5.8 Adsorption of Reactive Gases on Ice Surfaces 176
5.9 Ice-Water Interface 178
5.10 Ice Aqueous Solution Interface 182
5.11 Condensation, Deposition, and ThermalAccommodation Coefficients 184
CHAPTER 6 EQUILIBRIUM BEHAVIOR OF CLOUD DROPS AND ICEPARTICLES 188
6.1 General Equilibrium Relation for Two Phases Separatedby a Curved Interface 188
6.2 Effect of Curvature on Latent Heat of Phase Change 189
6.3 Generalized Clausius-Clapeyron Equation 190
6.4 Equilibrium Between a Pure Water Drop and Pure WaterVapor or Humid Air 191
6.5 Equilibrium Between an Aqueous Solution Drop andHumid Air 193
6.6 Equilibrium Between Humid Air and an AqueousSolution Drop Containing a Solid Insoluble Substance 196
6.7 Equilibrium Conditions for Ice Particles 199
6.8 Experimental Verification 205
CHAPTER 7 HOMOGENEOUS NUCLEATION 212
7.1 Homogeneous Nucleation of Water Drops and IceCrystals from Water Vapor 213
7.1.1 EQUILIBRIUM POPULATION OF EMBRYOS AND ENERGY OF EMBRYOFORMATION 213
7.1.2 THE NUCLEATION RATE J 220
7.1.3 EXPERIMENTAL VERIFICATION 225
7.2 Homogeneous Nucleation of Ice in Supercooled Water 226
7.2.1 THE NUCLEATION RATE J 226
7.2.2 THE ENERGY OF GERM FORMATION 228
7.2.3 THE MOLAR ACTIVATION ENERGY ~g* 230
CHAPTER 8 THE ATMOSPHERIC AEROSOL AND TRACE GASES 237
8.1 Gaseous Constituents of the Atmosphere 237
8.2 Atmospheric Aerosol Particles (AP) 246
8.2.1 FORMATION OF AEROSOL PARTICLES BY GAS TO PARTICLECONVERSION (GPC) 247
8.2.2 FORMATION OF AEROSOL PARTICLES BY DROP PARTICLE CONVERSION(DPC) 254
8.2.3 FORMATION OF AEROSOL PARTICLES BY BULK TO PARTICLECONVERSION (BPC) 261
8.2.4 AP FROM EXTRATERRE8TRIAL SOURCES 268
8.2.5 RATE OF EMISSION OF PARTICULATE MATTER INTO THE ATMOSPHERE 269
8.2.6 RESIDENCE TIME OF AP 269
8.2.7 WATER-SOLUBLE FRACTION OF AP 272
8.2.8 TOTAL MASS AND NUMBER CONCENTRATION OF AP 273
8.2.9 SIZE DISTRIBUTION OF AP 282
8.2.10 VERTICAL VARIATION OF THE NUMBER AND MASS CONCENTRATION 291
CHAPTER 9 HETEROGENEOUS NUCLEATION 308
9.1 Cloud Condensation Nuclei (CCN) 308
9.1.1 NUMBER CONCENTRATION AND CHEMICAL COMPOSITION OF CCN 308
9.1.2 MODE OF ACTION OF WATER-SOLUBLE AND MIXED CCN 317
9.1.3 NUCLEATION OF DROPS ON WATER-INSOLUBLE CCN 318
9.2 Ice Forming Nuclei (IN) 330
9.2.1 NUMBER CONCENTRATION OF IN 330
9.2.2 SOURCES AND CHEMICAL COMPOSITION OF IN 338
9.2.3 THE MAIN REQUIREMENTS FOR IN 347
9.2.4 THEORY OF HETEROGENEOUS ICE NUCLEATION 362
9.2.5 HETEROGENEOUS FREEZING OF SUPERCOOLED WATER DROPS 368
9.2.6 DISCREPANCY BETWEEN THE CONCENTRATIONS OF IN AND THECONCENTRATION OF ICE PARTICLES 376
CHAPTER 10 HYDRODYNAMICS OF SINGLE CLOUD AND PRECIPITATION PARTICLES 382
10.1 Basic Governing Equations 382
10.2 Flow Past a Rigid Sphere 385
10.2.1 CLASSIFICATION OF FLOWS ACCORDING TO REYNOLDS NUMBER 385
10.2.2 STEADY, AXISYMMETRIC FLOW 387
10.2.3 THE FALL BEHAVIOR OF RIGID SPHERES 405
10.2.4 NON-STEADY THREE-DIMENSIONAL FLOW 405
10.3 Hydrodynamic Behavior of Water Drops in Air 406
10.3.1 INTERNAL CIRCULATION IN DROPS 407
10.3.2 DROP SHAPE 414
10.3.3 DROP OSCILLATION 421
10.3.4 FALL BEHAVIOR OF DROPS 430
10.3.5 DROP INSTABILITY AND BREAKUP 431
10.3.6 TERMINAL VELOCITY OF WATER DROPS IN AIR 436
10.4 Hydrodynamic Behavior of Disks, Oblate Spheroids, andCylinders 442
10.4.1 CIRCULAR DISKS AND OBLATE SPHEROIDS 443
10.4.2 CIRCULAR CYLINDERS 449
10.5 Hydrodynamic Behavior of Snow Crystals, Snow Flakes,Graupel and Hailstones 454
10.5.1 FLOW FIELD AND DRAG 454
10.5.2 FALL VELOCITY 459
10.5.3 FALL PATTERN 465
CHAPTER 11 MECHANICS OF THE ATMOSPHERIC AEROSOL 468
11.1 Brownian Motion of Aerosol Particles 468
11.2 Particle Diffusion 470
11.3 Mobility and Drift Velocity 471
11.4 Sedimentation and the Vertical Distribution of AerosolParticles 472
11.5 Brownian Coagulation of Aerosol Particles 475
11.6 Laminar Shear, Turbulence, and GravitationalCoagulation 484
11.6.1 COAGULATION IN LAMINAR SHEAR FLOW 484
11.6.2 COAGULATION IN TURBULENT FLOW 486
11.6.3 GRAVITATIONAL COAGULATION 490
11.7 Explanation for the Observed Size Distributions of theAtmospheric Aerosol 493
11.7.1 QUASI-STATIONARY DISTRIBUTIONS (QSD) 493
11.7.2 SELF-PRESERVING DISTRIBUTIONS (SPD) 495
11.7.3 QUASI-STATIONARY SELF-PRESERVING DISTRIBUTIONS 501
11.7.4 STATISTICAL DISTRIBUTIONS 502
11.7.5 POWER LAW SOLUTIONS FOR A SOURCE-ENHANCED AEROSOL 503
CHAPTER 12 COOLING OF MOIST AIR 506
12.1 Water in the Atmosphere 506
12.2 Isobaric Cooling 509
12.3 Adiabatic Cooling of Unsaturated Air 509
12.4 The Thermodynamic Wetbulb Temperature 511
12.5 Lifting to Saturation and Beyond 511
12.6 Adiabatic Cooling of Saturated Air 513
12.7 Cooling with Entrainment 513
12.8 The Concept of Entrainment 514
12.9 The Air Parcel Model for a Convective Cloud 518
CHAPTER 13 DIFFUSION GROWTH AND EVAPORATION OF WATER DROPSAND SNOW CRYSTALS 523
13.1 Laws for Diffusion of Water Vapor and Heat 523
13.1.1 DIFFUSION OF WATER VAPOR 523
13.1.2 DIFFUSION OF HEAT 528
13.2 Growth of Aqueous Solution Drops by Diffusion ofWater Vapor 530
13.2.1 GROWTH OF AN INDIVIDUAL STATIONARY DROP 530
13.2.2 DIFFUSIONAL GROWTH OF A POPULATION OF SOLUTION DROPSOF NEGLIBLE FALL VELOCITY 533
13.2.3 STEADY STATE EVAPORATION OF WATER DROPS FALLING IN SUBSATURATED AIR 558
13.3 Growth of Snow Crystals by Diffusion of Water Vapor 567
13.3.1 GROWTH OF A STATIONARY SNOW CRYSTAL 567
13.3.2 GROWTH OF A VENTILATED SNOW CRYSTAL 571
13.3.3 GROWTH RATE OF SNOW CRYSTAL FACES - SNOW CRYSTAL HABIT CHANGE 582
CHAPTER 14 CLOUD PARTICLE INTERACTIONS 589
14.1 The Basic Model for Drop Collisions 589
14.2 Definition of Collision Efficiency 590
14.3 The Superposition Method 592
14.4 The Boundary Value Problem Approach 595
14.4.1 THE QUASI-STATIONARY ASSUMPTION 595
14.4.2 Two SPHERES IN STEADY STOKES FLOW 596
14.4.3 THE SLIP-FLOW CORRECTION IN STOKES FLOW 598
14.4.4 Two SPHERES IN MODIFIED OSEEN FLOW 600
14.5 Collision of Water Drops with Water Drops 602
14.5.1 THE CASE OF CALM AIR 602
14.5.2 THE CASE OF TURBULENT AIR 605
14.5.3 EXPERIMENTAL VERIFICATION 612
14.5.4 COALESCENCE OF WATER DROPS IN AIR 615
14.6 Collision of Snow Crystals with Water Drops 620
14.6.1 COLLISION OF LARGE SNOW CRYSTALS WITH SMALL DROPS 620
14.6.2 COLLISION OF LARGE DROPS WITH SMALL SNOW CRYSTALS 627
14.7 Collision of Snow Crystals with Snow Crystals 628
14.8 Orientation Model for Particles in Turbulence 631
14.8.1 TURBULENCE MODEL 632
14.8.2 ORIENTATION OF SPHEROIDS IN TURBULENT AIR 632
14.8.3 GENERALIZED ORIENTATION DISTRIBUTION 634
CHAPTER 15 GROWTH OF CLOUD DROPS BY COLLISION, COALESCENCE AND BREAKUP 638
15.1 Continuous Model for Collection Growth 638
15.2 Polynomial Approximations to the GravitationalCollection Kernel 641
15.3 Stochastic Model for Collisional Growth 643
15.3.1 COMPLETENESS OF THE SCE 645
15.3.2 EXACT SOLUTIONS TO THE SCE 651
15.3.3 NUMERICAL AND ApPROXIMATION TECHNIQUES FOR THE SCE 657
15.4 Stochastic Model for Drop Breakup 666
15.5 Stochastic Drop Growth in Combination with StochasticDrop Breakup 671
CHAPTER 16 GROWTH OF ICE PARTICLES BY ACCRETION AND ICE PARTICLE MELTING 680
16.1 Growth of Ice Particles by Accretion of SupercooledDrops 680
16.1.1 GROWTH MODE AND STRUCTURE OF RIMED ICE PARTICLES,GRAUPEL, AND HAILSTONES 680
16.1.2 STRUCTURE AND GROWTH MODE OF ICE IN SUPERCOOLED WATER 684
16.1.3 GROWTH RATE OF ICE IN SUPERCOOLED WATER 689
16.1.4 FREEZING TIME OF WATER DROPS 695
16.1.5 GROWTH RATE OF GRAUPEL AND HAILSTONES 700
16.1.6 SNOW CRYSTAL MULTIPLICATION BY RIMING 708
16.2 Growth of Snow Crystals by Collision with other SnowCrystals 710
16.3 Melting of Ice Particles 712
16.3.1 MELTING OF GRAUPEL AND HAILSTONES 713
16.3.2 MELTING OF SNOW FLAKES 718
CHAPTER17 CLOUD CHEMISTRY 721
17.1 Concentrations of Water Soluble Compounds in BulkCloud and Rain Water, and in Bulk Water of MeltedSnow 722
17.2 Concentration of Water Insoluble Particles in BulkCloud and Rain Water and Bulk Water of Melted Snow 729
17.3 Concentration of Water Soluble Compounds inIndividual Cloud and Raindrops 732
17.4 Scavenging of Aerosol Particles by Cloud Drops,Raindrops and Ice Particles 736
17.4.1 NUCLEATION SCAVENGING 737
17.4.2 IMPACTION SCAVENGING 741
17.5 Scavenging of Gases by Cloud Drops, Raindrops and IceParticles 765
17.5.1 SCAVENGING OF GASES BY WATER DROPS 770
17.5.2 ASYMMETRY BETWEEN ABSORPTION AND DESORPTION OF GASES 796
17.5.3 DEVIATIONS FROM EQUILIBRIUM 798
17.5.4 SCAVENGING OF GASES BY ICE PARTICLES 804
17.6 The Scavenging Parameters 805
17.7 Wet Deposition 808
CHAPTER 18 CLOUD ELECTRICITY 813
18.1 Electrical State of the Cloudless Atmosphere 813
18.2 Electrical State of the Atmospheric Aerosol 816
18.3 Electrical Conductivity in Clouds 819
18.3.1 DIFFUSION AND CONDUCTION OF IONS TO CLOUD DROPS 819
18.3.2 CONDUCTIVITY IN WEAKLY ELECTRIFIED CLOUDS 820
18.3.3 CONDUCTIVITY IN STRONGLY ELECTRIFIED CLOUDS 823
18.4 Charge Distribution in Clouds 825
18.4.1 WEAKLY ELECTRIFIED CLOUDS 825
18.4.2 STRONGLY ELECTRIFIED CLOUDS 827
18.5 Cloud Charging Mechanisms 832
18.5.1 REQUIREMENTS FOR A CLOUD CHARGING MECHANISM 832
18.5.2 THE MAJOR CLOUD CHARGING MECHANISMS 833
18.6 Effect of Electric Fields and Charges on MicrophysicalProcesses 848
18.6.1 DROP AND ICE CRYSTAL NUCLEATION 848
18.6.2 DIFFUSIONAL GROWTH OF ICE CRYSTALS 849
18.6.3 DROP DEFORMATION, DISRUPTION AND CORONA PRODUCTION 850
18.6.4 DROP TERMINAL VELOCITIES 856
18.6.5 COLLISIONAL GROWTH RATE OF CLOUD PARTICLES 857
18.6.6 SCAVENGING OF AEROSOL PARTICLES 867
APPENDICES 874
REFERENCES 895
LIST OF PRINCIPAL SYMBOLS 956
TABLE OF PHYSICAL CONSTANTS 965
INDEX 966