Chapter 1 Fundamentals of Radiation for Atmospheric Applications

1.1 Concepts, Definitions, and Units

1.1.1 Electromagnetic Spectrum
1.1.2 Solid Angle
1.1.3 Basic Radiometric Quantities
1.1.4 Concepts of Scattering and Absorption

1.2 Blackbody Radiation Laws

1.2.1 Planck's Law
1.2.2 Stefan-Boltzmann Law
1.2.3 Wien's Displacement Law
1.2.4 Kirchhoff's Law

1.3 Absorption Line Formation and Line Shape

1.3.1 Line Formation

1.3.1.1 Bohr's Model
1.3.1.2 Vibrational and Rotational Transitions

1.3.2 Line Broadening

1.3.2.1 Pressure Broadening
1.3.2.2 Doppler Broadening
1.3.2.3 Voigt Profile

1.3.3 Breakdown of Thermodynamic Equilibrium

1.4 Introduction to Radiative Transfer

1.4.1 The Equation of Radiative Transfer
1.4.2 Beer-Bouguer-Lambert Law
1.4.3 Schwarzschild's Equation and its Solution
1.4.4 The Equation of Radiative Transfer for Plane-Parallel Atmospheres
1.4.5 Radiative Transfer Equations for Three-Dimensional Inhomogeneous Media
Exercises
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Chapter 2 Solar Radiation at the Top of the Atmosphere

2.1 The Sun as an Energy Source

2.1.1 The Structure of the Sun
2.1.2 Solar Surface Activities: Sunspots

2.2 The Earth's Orbit About the Sun and Solar Insolation

2.2.1 Orbital Geometry
2.2.2 Definition of the Solar Constant
2.2.3 Distribution of Solar Insolation

2.3 Solar Spectrum and Solar Constant Determination

2.3.1 Solar Spectrum
2.3.2 Determination of the Solar Constant: Ground-Based Method
2.3.3 Satellite Measurements of the Solar Constant
Exercises
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Chapter 3 Absorption and Scattering of Solar Radiation in the Atmosphere

3.1 Composition and Structure of the Earth's Atmosphere

3.1.1 Thermal Structure
3.1.2 Chemical Composition

3.2 Atmospheric Absorption

3.2.1 Absorption in the Ultraviolet

3.2.1.1 Molecular Nitrogen
3.2.1.2 Molecular Oxygen
3.2.1.3 Ozone
3.2.1.4 Other Minor Gases
3.2.1.5 Absorption of Solar Radiation

3.2.2 Photochemical Processes and the Formation of Ozone Layers
3.2.3 Absorption in the Visible and Near Infrared

3.2.3.1 Molecular Oxygen and Ozone
3.2.3.2 Water Vapor
3.2.3.3 Carbon Dioxide
3.2.3.4 Other Minor Gases
3.2.3.5 Transfer of Direct Solar Flux in the Atmosphere

3.3 Atmospheric Scattering

3.3.1 Rayleigh Scattering

3.3.1.1 Theoretical development
3.3.1.2 Phase function, Scattering Cross Section, and Polarizability
3.3.1.3 Blue Sky and Sky Polarization

3.3.2 Light Scattering by Particulates: Approximations

3.3.2.1 Lorenz-Mie Scattering
3.3.2.2 Geometric Optics
3.3.2.3 Anomalous Diffraction Theory

3.4 Multiple Scattering and Absorption in Planetary AtmospheresTMOSPHERES

3.4.1 Fundamentals of Radiative Transfer
3.4.2 Approximations of Radiative Transfer

3.4.2.1 Single-Scattering Approximation
3.4.2.2 Diffusion Approximation

3.5 Atmospheric Solar Heating Rates
Exercises
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Chapter 4 Thermal Infrared Radiative Transfer in the Atmosphere

4.1 The Thermal Infrared Spectrum and the Greenhouse Effect
4.2 Absorption and Emission in the Atmosphere

4.2.1 Absorption in the Thermal Infrared

4.2.1.1 Water Vapor
4.2.1.2 Carbon Dioxide
4.2.1.3 Ozone
4.2.1.4 Methane
4.2.1.5 Nitrous Oxide
4.2.1.6 Chlorofluorocarbons

4.2.2 Fundamentals of Thermal Infrared Radiative Transfer
4.2.3 Line-by-Line (LBL) Integration

4.3 Correlated K-Distribution Method for Infrared Radiative Transfer

4.3.1 Fundamentals
4.3.2 Application to Nonhomogeneous Atmospheres
4.3.3 Numerical Procedures and Pertinent Results
4.3.4 Line Overlap Consideration

4.4 Band Models

4.4.1 A Single Line
4.4.2 Regular Band Model
4.4.3 Statistical Band Model
4.4.4 Application to Nonhomogeneous Atmospheres

4.5 Broadband Approaches to Flux Computations

4.5.1 Broadband Emissivity
4.5.2 Newtonian Cooling Approximation

4.6 Infrared Radiative Transfer in Cloudy Atmospheres

4.6.1 Fundamentals
4.6.2 Exchange of Infrared Radiation Between Cloud and Surface
4.6.3 Two/Four-Stream Approximations

4.7 Atmospheric Infrared Cooling Rates
Exercises
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Chapter 5 Light Scattering by Atmospheric Particulates

5.1 Morphology of Atmospheric Particulates
5.2 Lorenz-Mie Theory of Light Scattering by Spherical Particles

5.2.1 Electromagnetic Wave Equation and Solution
5.2.2 Formal Scattering Solution
5.2.3 The Far-Field Solution and Extinction Parameters
5.2.4 Scattering Phase Matrix for Spherical Particles

5.3 Geometric Optics

5.3.1 Diffraction
5.3.2 Geometric Reflection and Refraction
5.3.3 Geometric Optics, Lorenz-Mie Theory, and Representative Results

5.4 Light Scattering by Ice Crystals: A Unified Theory

5.4.1 Geometric Optics for Ice Crystals

5.4.1.1 Conventional Approach
5.4.1.2 Improved Geometric Optics Approach
5.4.1.3 Absorption Effects in Geometric Optics
5.4.1.4 Monte Carlo Method for Ray Tracing

5.4.2 Introduction to the Finite-Difference Time Domain Method
5.4.3 Scattering Phase Matrix for Nonspherical Ice Particles
5.4.4 Presentation of a Unified Theory for Light Scattering by Ice Crystals

5.4.4.1 The Essence of the Unified Theory
5.4.4.2 Theory Versus Measurement and Representative Results

5.5 Light Scattering by Nonspherical Aerosols

5.5.1 Finite-Difference Time Domain Method
5.5.2 T-Matrix Method
5.5.3 Note on Light-Scattering Measurements for Nonspherical Aerosols
Exercises
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Chapter 6 Principles of Radiative Transfer in Planetary Atmospheres

6.1 Introduction

6.1.1 A Brief History of Radiative Transfer
6.1.2 Basic Equations for the Plane-Parallel Condition

6.2 Discrete-Ordinates Method for Radiative Transfer

6.2.1 General Solution for Isotropic Scattering
6.2.2 The Law of Diffuse Reflection for Semi-Infinite Isotropic Scattering Atmospheres
6.2.3 General Solution for Anisotropic Scattering
6.2.4 Application to Nonhomogeneous Atmospheres

6.3 Principles of Invariance

6.3.1 Definitions of Scattering Parameters
6.3.2 Principles of Invariance for Semi-Infinite Atmospheres
6.3.3 Principles of Invariance for Finite Atmospheres
6.3.4 The X and Y Functions
6.3.5 Inclusion of Surface Reflection

6.4 Adding Method for Radiative Transfer

6.4.1 Definitions of Physical Parameters
6.4.2 Adding Equations
6.4.3 Equivalence of the Adding Method and the Principles of Invariance
6.4.4 Extension to Nonhomogeneous Atmospheres for Internal Fields
6.4.5 Similarity Between the Adding and Discrete-Ordinates Methods

6.5 Approximations for Radiative Transfer

6.5.1 Successive Order-of-Scattering Approximation
6.5.2 Two-Stream and Eddington's Approximations
6.5.3 Delta-Function Adjustment and Similarity Principle
6.5.4 Four-Stream Approximation

6.6 Radiative Transfer Including Polarization

6.6.1 Representation of Light Beam
6.6.2 Formulation

6.7 Advanced Topics in Radiative Transfer

6.7.1 Horizontally Oriented Ice Particles
6.7.2 Three-Dimensional Nonhomogeneous Clouds

6.7.2.1 Monte Carlo Method
6.7.2.2 Successive Order-of-Scattering (SOS)Approach
6.7.2.3 Delta Four-Term (Diffusion) Approximation

6.7.3 Spherical Atmospheres
Exercises
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Chapter 7 Application of Radiative Transfer Principles to Remote Sensing

7.1 Introduction
7.2 Remote Sensing Using Transmitted Sunlight

7.2.1 Determination of Aerosol Optical Depth and Size Distribution

7.2.1.1 Direct Linear Inversion
7.2.1.2 Constrained Linear Inversion

7.2.2 Determination of Total Ozone Concentration
7.2.3 Limb Extinction Technique

7.3 Remote Sensing Using Reflected Sunlight

7.3.1 Satellite-Sun Geometry and Theoretical Foundation
7.3.2 Satellite Remote Sensing of Ozone
7.3.3 Satellite Remote Sensing of Aerosols
7.3.4 Satellite Remote Sensing of Land Surfaces
7.3.5 Cloud Optical Depth and Particle Size

7.3.5.1 BidirectionalRreflectance
7.3.5.2 Polarization
7.3.5.3 Reflected Line Spectrum

7.4 Remote Sensing Using Emitted Infrared Radiation

7.4.1 Theoretical Foundation
7.4.2 Surface Temperature Determination
7.4.3 Remote Sensing of Temperature Profiles

7.4.3.1 Nonlinear Iteration Method
7.4.3.2 Minimum Variance Method: Hybrid Retrieval
7.4.3.3 Cloud Removal

7.4.4 Remote Sensing of Water Vapor and Trace Gas Profiles

7.4.4.1 WaterVvapor from the 6.3 µmVvibrational-Rotational Band
7.4.4.2 Limb Scanning Technique

7.4.5 Infrared Remote Sensing of Clouds

7.4.5.1 Carbon Dioxide Slicing Technique for Cloud Top Pressure and Emissivity
7.4.5.2 Emitted Radiance for Cloud Cover
7.4.5.3 Retrieval of Cirrus Cloud Optical Depth and Temperature
7.4.5.4 Information Content in Infrared Line Spectrum

7.4.6 Remote Sensing of Infrared Cooling Rate and Surface Flux

7.5 Remote Sensing Using Emitted Microwave Radiation

7.5.1 Microwave Spectrum and Microwave Radiative Transfer
7.5.2 Rainfall Rate and Water Vapor Determination from Microwave Emission
7.5.3 Temperature Retrieval from Microwave Sounders

7.6 Remote Sensing Using Laser and Microwave Energy

7.6.1 Backscattering Equation: Theoretical Foundation
7.6.2 Lidar Differential Absorption and Depolarization Techniques

7.6.2.1 Differential absorption technique
7.6.2.2 Principle of depolarization

7.6.3 Millimeter-Wave Radar for Cloud Study

Exercises
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Chapter 8 Radiation and Climate

8.1 Introduction

8.2 Radiation Budgets of the Earth-Atmosphere System

8.2.1 Observational Considerations

8.2.1.1 Black and White Sensors Based on Radiative Equilibrium
8.2.1.2 Scanning Radiometer and Angular Models

8.2.2 Radiation Budget Viewed from Space
8.2.3 Cloud Radiative Forcing Derived from ERB Data
8.2.4 Radiative Heating/Cooling Rates of the Atmosphere
8.2.5 Radiation Budget at the Surface

8.3 Radiative and Convective Atmospheres

8.3.1 Radiative Equilibrium

8.3.1.1 A Gglobal Model
8.3.1.2 A Vertical Model

8.3.2 Radiative and Convective Equilibrium

8.3.2.1 Heat Budget of the Earth-Atmosphere System
8.3.2.2 Convective Adjustment

8.4 Radiation in One-Dimensional Climate Models

8.4.1 Carbon Dioxide Greenhouse Effects
8.4.2 Ozone and Other Greenhouse Gases

8.4.2.1 Ozone
8.4.2.2 Methane
8.4.2.3 Nitrous Oxide
8.4.2.4 Halocarbons

8.4.3 Radiation Feedback Consideration
8.4.4 Aerosols and Radiation
8.4.5 Cloud Radiative Forcing

8.4.5.1 Cloud Position and Cover
8.4.5.2 Cloud Microphysics
8.4.5.3 Aerosols/Clouds and Precipitation

8.5 Radiation in Energy Balance Climate Models

8.5.1 Energy Budget of the Atmosphere and the Surface

8.5.1.1 Atmosphere and Oceans
8.5.1.2 Surface Energy Budget

8.5.2 Radiative Forcing in Energy Balance Climate Models

8.5.2.1 Linear Heating Approach
8.5.2.2 Diffusion Approach

8.5.3 Solar Insolation Perturbation

8.6 Radiation in Global Climate Models

8.6.1 An Introduction to General Circulation Modeling
8.6.2 Cloud Radiative Forcing in Global Climate Models

8.6.2.1 Internal Radiative Forcing
8.6.2.2 Greenhouse Warming and Cloud Cover Feedback
8.6.2.3 Greenhouse Warming and Cloud Liquid/Ice Water Content Feedback
8.6.2.4 Cloud Particle Size Feedback

8.6.3 Direct Radiative Forcing: Aerosols and Contrails

8.6.3.1 Aerosols
8.6.3.2 Contrails

8.6.4 Radiation in El Niño-Southern Oscillation
Exercises
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Appendix A Derivation of the Planck Function
Appendix B The Schrödinger Wave Equation
Appendix C Spherical Geometry
Appendix D Complex Index of Refraction, Dispersion of Light, and Lorentz-Lorenz Formula
Appendix E Properties of the Legendre Polynomials and Addition Theorem
Appendix F Some Useful Constants
Appendix G Standard Atmospheric Profiles
Appendix H Answers to Selected Exercises
References
Index
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