Microphysics of Clouds and Precipitation

Cloud physics has achieved such a voluminous literature over the past few decades that a significant quantitative study of the entire field would prove unwieldy. This book concentrates on one major aspect: cloud microphysics, which involves the processes that lead to the formation of individual cloud and precipitation particles. Common practice has shown that one may distinguish among the following additional major aspects: cloud dynamics, which is concerned with the physics responsible for the macroscopic features of clouds; cloud electricity, which deals with the electrical structure of clouds and the electrification processes of cloud and precipitation particles; and cloud optics and radar meteorology, which describe the effects of electromagnetic waves interacting with clouds and precipitation. Another field intimately related to cloud physics is atmospheric chemistry, which involves the chemical composition of the atmosphere and the life cycle and characteristics of its gaseous and particulate constituents. In view of the natural interdependence of the various aspects of cloud physics, the subject of microphysics cannot be discussed very meaningfully out of context. Therefore, we have found it necessary to touch briefly upon a few simple and basic concepts of cloud dynamics and thermodynamics, and to provide an account of the major characteristics of atmospheric aerosol particles. We have also included a separate chapter on some of the effects of electric fields and charges on the precipitation-forming processes.

1 Historical Review.- 2 Microstructure of Atmospheric Clouds and Precipitation.- 2.1 Microstructure of Clouds and Precipitation Consisting of Water Drops.- 2.1.1 Clouds and Fogs.- 2.1.2 Rain.- 2.2 Microstructure of Cloud and Precipitation Consisting of Ice Particles.- 2.2.1 Shape, Dimensions, Bulk Density, and Number Concentration of Ice Crystals.- 2.2.2 Shape, Dimensions, Bulk Density, and Number Concentration of Snowflakes, Graupel, and Hailstones.- 3 The Structure of Water Substance.- 3.1 Structure of an Isolated Water Molecule.- 3.2 Structure of Water Vapor.- 3.3 Structure of Ice.- 3.4 Structure of Water and Aqueous Solutions.- 4 Equilibrium Between Water Vapor, Water, Aqueous Solutions, and Ice in Bulk.- 4.1 Useful Thermodynamic Relations.- 4.2 General Conditions for Equilibrium.- 4.3 Phase Rule.- 4.4 Ideal Versus Real Behavior of Dry Air, Water Vapor, and Moist Air.- 4.5 Chemical Potential of Water Vapor in Humid Air, and of Water in Aqueous Solutions.- 4.6 Equilibrium Between an Aqueous Salt Solution and Water Vapor.- 4.7 Bulk Density of Ice, Water, and Aqueous Solutions.- 4.8 Latent Heat of Phase Change and its Temperature Variation.- 4.9 Clausius-Clapeyron Equation.- 4.10 Equilibrium Between an Aqueous Salt Solution and Ice.- 5 Surface Properties of Water Substance.- 5.1 Surface Tension.- 5.2 Equilibrium Conditions.- 5.3 Phase Rule for Systems with Curved Interfaces.- 5.4 Water-Vapor Interface.- 5.4.1 Effect of Temperature on Surface Tension.- 5.4.2 Surface Tension of a Salt Solution.- 5.4.3 Radius Dependence of Surface Tension.- 5.5 Angle of Contact.- 5.6 Adsorption of Gases onto Solid Surfaces.- 5.7 Ice-Vapor Interface.- 5.7.1 Surface Energy of Ice.- 5.7.2 Wulff’s Theorem.- 5.7.3 Real Ice Surfaces.- 5.8 Ice-Water and Ice-Aqueous Solution Interfaces.- 5.9 Condensation, Deposition, and Thermal Accommodation Coefficients.- 6 Equilibrium Behavior of Cloud Drops and Ice Particles.- 6.1 General Equilibrium Relation for Two Phases Separated by a Curved Interface.- 6.2 Effect of Curvature on Latent Heat of Phase Change.- 6.3 Generalized Clausius-Clapeyron Equation.- 6.4 Equilibrium Between a Pure Water Drop and Pure Water Vapor or Humid Air.- 6.5 Equilibrium Between an Aqueous Solution Drop and Humid Air.- 6.6 Equilibrium Between Humid Air and an Aqueous Solution Drop Containing a Solid Insoluble Substance.- 6.7 Equilibrium Conditions for Ice Particles.- 6.8 Experimental Verification.- 6.9 Equilibrium Growth of Atmospheric Aerosol Particles.- 7 Homogeneous Nucleation.- 7.1 Equilibrium Population of Embryos.- 7.1.1 Formal Statistical Mechanics Description.- 7.1.2 Classical Description.- 7.1.3 Modified Classical Description.- 7.1.4 Molecular Model Method.- 7.2 Nucleation Rate J.- 7.2.1 Equilibrium Approximation for J.- 7.2.2 Steady State Rate Approximation for J.- 7.3 Experimental Verification.- 8 The Atmospheric Aerosol.- 8.1 Gaseous Constituents of the Atmosphere.- 8.2 Atmospheric Aerosol Particles (AP).- 8.2.1 Formation of AP by Gas-to-Particle Conversion (GPC).- 8.2.2 Formation of AP by Mechanical and Chemical Disintegration and Dispersal at the Solid Earth Surface.- 8.2.3 Formation of AP by Mechanical Disintegration and Dispersal at the Surface of Oceans.- 8.2.4 AP from Extraterrestrial Sources.- 8.2.5 Rate of Emission of Particulate Matter into the Atmosphere.- 8.2.6 Residence Time (? AP) of AP.- 8.2.7 Water-Soluble Fraction of AP.- 8.2.8 Total Concentration and Vertical Variation of AP over Land.- 8.2.9 Total Concentration and Vertical Variation of AP over Oceans.- 8.2.10 Size Distribution of AP.- 8.3 Aerosol Substances in Cloud and Precipitation Water.- 9 Heterogeneous Nucleation.- 9.1 Cloud Condensation Nuclei (CCN).- 9.1.1 Number Concentration of CCN.- 9.1.2 Mode of Action of Water-Soluble and Mixed CCN.- 9.1.3 Nucleation on Water-Insoluble. Partially Wettable CCN.- 9.1.3.1 Nucleation on a Planar Substrate.- 9.1.3.2 Nucleation on a Curved Substrate.- 9.1.4 Experimental Verification of Heterogeneous Water Drop Nucleation.- 9.2 Ice Forming Nuclei (IN).- 9.2.1 Number Concentration of IN.- 9.2.2 Sources of IN.- 9.2.3 Characteristic Features and Mode of Action of IN.- 9.2.3.1 Insolubility Requirement.- 9.2.3.2 Size Requirement.- 9.2.3.3 Chemical Bond Requirement.- 9.2.3.4 Crystallographic Requirement.- 9.2.3.5 Active-Site Requirement.- 9.2.4 Theory of Heterogeneous Ice Nucleation.- 9.2.4.1 Classical Model.- 9.2.4.2 Extensions of the Classical Model.- 9.2.5 Heterogeneous Freezing of Supercooled Water Drops.- 9.2.6 Heterogeneous Freezing of Supercooled Aqueous Solution Drops.- 10 Hydrodynamics of Single Cloud and Precipitation Particles.- 10.1 Basic Governing Equations.- 10.2 Flow Past a Rigid Sphere.- 10.2.1 Classification of Flows According to Reynolds Number.- 10.2.2 Stream Function.- 10.2.3 The Drag Problem.- 10.2.4 Analytical Solutions for the Sphere.- 10.2.5 Numerical Approach to the Navier-Stokes Equation.- 10.2.6 Comparison of Analytical and Numerical Solutions of the Navier-Stokes Equation with Experimental Results.- 10.3 Hydrodynamic Behavior of Water Drops in Air.- 10.3.1 Internal Circulation in Drops.- 10.3.2 Shape of Water Drops.- 10.3.3 Drop Oscillation.- 10.3.4 Drop Instability and Breakup.- 10.3.5 Terminal Velocity of Water Drops in Air.- 10.4 Hydrodynamic Behavior of Disks, Oblate Spheroids, and Cylinders.- 10.4.1 Circular Disks and Oblate Spheroids.- 10.4.2 Circular Cylinders.- 10.5 Motion of Ice Crystals, Snowflakes, Graupel, and Hailstones.- 11 Cooling of Moist Air.- 11.1 Water in the Atmosphere.- 11.2 Isobaric Cooling.- 11.3 Adiabatic Cooling of Unsaturated Air.- 11.4 Adiabatic Cooling of Saturated Air.- 11.5 Cooling with Entrainment.- 11.6 Governing Equations for a One-Dimensional Cloud.- 12 Mechanics of the Atmospheric Aerosol.- 12.1 Brownian Motion of Aerosol Particles.- 12.2 Particle Diffusion.- 12.3 Mobility and Drift Velocity.- 12.4 Sedimentation and the Vertical Distribution of Aerosol Particles.- 12.5 Brownian Coagulation of Aerosol Particles.- 12.6 Laminar Shear, Turbulence, and Gravitational Coagulation.- 12.6.1 Coagulation in Laminar Shear Flow.- 12.6.2 Coagulation in Turbulent Flow.- 12.6.2.1 Turbulent Shear Coagulation.- 12.6.2.2 Turbulent Inertial Coagulation.- 12.6.3 Gravitational Coagulation.- 12.7 Scavenging of Aerosols.- 12.7.1 Scavenging by Convective Diffusion.- 12.7.2 Scavenging by Thermophoresis and Diffusiophoresis.- 12.7.3 Scavenging by Turbulence.- 12.7.4 Scavenging by Gravitational or Inertial Impaction.- 12.7.5 Overall Scavenging Effects.- 12.8 Explanations for the Observed Size Distribution of the Atmospheric Aerosol.- 12.8.1 Quasi-Stationary Distributions (QSD).- 12.8.2 Self-Preserving Distributions (SPD).- 12.8.3 Quasi-Stationary Self-Preserving Distributions.- 12.8.4 Statistical Distributions.- 12.8.5 Power Law Solutions for a Source-Enhanced Aerosol.- 13 Diffusion Growth and Evaporation of Water Drops and Ice Crystals.- 13.1 Laws for Diffusion of Water Vapor and Heat.- 13.1.1 Diffusion of Water Vapor.- 13.1.2 Diffusion of Heat.- 13.2 Diffusional Growth of Aqueous Solution Drops.- 13.2.1 Growth of an Individual Stationary Drop.- 13.2.2 Diffusional Growth of a Population of Solution Drops of Negligible Fall Velocity.- 13.2.2.1 Condensation Growth in Cumuliform Clouds.- 13.2.2.2 Condensation Growth in Stratiform Clouds.- 13.2.3 Steady State Evaporation of Water Drops Falling in Subsa-turated Air.- 13.3 Diffusional Growth of Ice Crystals.- 13.3.1 Growth of a Stationary Ice Crystal.- 13.3.2 Growth of a Ventilated Ice Crystal.- 13.3.3 Growth Rate of Ice Crystal Faces-Ice Crystal Habit Change.- 14 Cloud Particle Interactions-Collision, Coalescence, and Breakup.- 14.1 The Basic Model for Drop Collisions.- 14.2 Definition of Collision Efficiency.- 14.3 The Superposition Method.- 14.4 The Boundary Value Problem Approach.- 14.4.1 The Quasi-Stationary Assumption.- 14.4.2 Two Spheres in Steady Stokes Flow.- 14.4.3 The Slip-Flow Correction in Stokes Flow.- 14.4.4 Two Spheres in Modified Oseen Flow.- 14.5 Enhancement of Gravitational Collection by Turbulence.- 14.6 Theoretical Collision Efficiencies of Water Drops in Air.- 14.6.1 The Case of Calm Air.- 14.6.2 The Case of Turbulent Air.- 14.7 Experimental Verification.- 14.8 Coalescence of Water Drops in Air.- 14.8.1 The Rebound Problem.- 14.8.2 Disruption Following Coalescence.- 14.9 Collisions of Ice Crystals with Water Drops.- 14.10 Collisions of Ice Crystals with Ice Crystals.- 15 Growth of Cloud Drops by Collision and Coalescence.- 15.1 Continuous Model for Collection Growth.- 15.2 Stochastic Model for Collection Growth.- 15.2.1 Completeness of the SCE.- 15.2.1.1 Three Models for Collection Growth.- 15.2.1.2 Correlations in a Stochastic Coalescence Process.- 15.2.2 Exact Solutions to the SCE.- 15.2.3 Approximation Techniques for the SCE.- 15.2.3.1 Method of Moments.- 15.2.3.2 Polynomial Approximations to the Gravitational Collection Kernel.- 15.2.4 Numerical Methods for the Collection Process.- 15.2.4.1 Method for Berry (1967) and Reinhardt (1972).- 15.2.4.2 Method of Kovetz and Olund (1969).- 15.2.4.3 Monte Carlo Method.- 15.2.5 Parameterization of the Collection Process.- 15.3 Representative Numerical Results for the Collection Process.- 15.4 Collection Growth with Condensation and Breakup.- 16 Microphysics of Ice Particle-Drop Interactions.- 16.1 Growth Mode and Structure of Rimed Ice Particles, Graupel, and Hailstones.- 16.2 Freezing Time of Water Drops.- 16.3 Structure and Growth Mode of Ice in Supercooled Water.- 16.4 Growth Rate of Ice in Supercooled Water.- 16.5 Growth Rate of Graupel and Hailstones.- 16.6 Ice Particle Multiplication Processes.- 16.7 Melting of Ice Particles.- 17 The Electrical State Of the Atmosphere and Its Effects on Cloud Microphysics.- 17.1 Electrical State of the Cloudless Atmosphere.- 17.2 Electrical State of the Atmospheric Aerosol.- 17.3 Electrical Conductivity in Clouds.- 17.3.1 Diffusion and Conduction of Ions to Cloud Drops.- 17.3.2 Conductivity in Weakly Electrified Clouds.- 17.3.3 Conductivity in Strongly Electrified Clouds.- 17.4 Cloud Electrification.- 17.4.1 Weakly Electrified Clouds.- 17.4.2 Strongly Electrified Clouds.- 17.4.2.1 Observed Charges and Fields.- 17.4.2.2 Models for Cloud Electrification.- 17.5 Effect of Electric Fields and Charges on Microphysical Processes.- 17.5.1 Drop and Ice Crystal Nucleation.- 17.5.2 Diffusional Growth of Ice Crystals.- 17.5.3 Drop Disruption and Corona Production.- 17.5.4 Drop Terminal Velocities.- 17.5.5 Collisional Growth Rate of Cloud Particles.- 17.5.6 Scavenging of Aerosol Particles.- Appendices.- A-4.9 Convenient Formulations for Determining the Saturation Vapor Pressure Over Water and Ice (Lowe and Ficke, 1974).- A-7.1 Relations from Statistical Mechanics.- A-10.1 Equations of Fluid Flow.- A-10.2.2 Stream Function Formulation for Axisymmetric, Incompressible Flow.- A-10.3.3 Drop Oscillations.- A-10.3.4 Rayleigh-Taylor Instability of Two Superposed Fluids.- A-12.4 Mutual Sedimentation and Diffusion of Aerosol Particles.- A-14.1 Nearest Neighbor Distance Between Cloud Drops.- A-14.3 Superposition Method for Stokes Flow.- A-14.4.2 Special Problems 1, 2, 3 for Two Spheres in Steady State Stokes Row.- A-14.4.3 Details of the Slip-Flow Correction.- A-14.4.4 Flow Field and Forces for Two Spheres in Modified Oseen Flow.- A-14.5 Drop Interactions in Turbulent Air (de Almeida, 1975).- A-15.2.1.2 Correlations in a Stochastic Coalescence Process (Bayewitz et al. 1974).- A-15.2.2 Particular Solutions to the SCE.- A-15.2.4.3 A Monte Carlo Algorithm for Stochastic Coalescence.- A-15.2.5 Parameterization of Accretion and Hydrometeor Self-Collection.- A-17.5.5 Two Charged Conducting Spheres in a Background Electric Field.- References.- List of Principal Symbols.- Table of Physical Constants.- Index of Subjects.