Atmospheric Radiation: A Primer with Illustrative Solutions

A first–look at radiative transfer in planetary atmospheres with a particular focus on the Earth′s atmosphere and climate. The textbook covers the basics of the radiative transfer of sunlight, treating absorption and scattering, and the transfer of the thermal infrared appropriate for local thermodynamic equilibrium, absorption and emission. The examples included show how the solutions of the radiative transfer equation are used in remote sensing to probe the thermal structure and composition of planetary atmospheres. This motivates students by leading them to a better understanding of and appreciation for the computer–generated numerical results. Aimed at upper–division undergraduates and beginning graduate students in physics and atmospheric sciences, the book is designed to cover the essence of the material in a 10–week course, while the material in the optional sections will facilitate its use at the more leisurely pace and in–depth focus of a semester course.

Preface IX 1 The Earth’s Energy Budget and Climate Change 1 1.1 Introduction 1 1.2 Radiative Heating of the Atmosphere 2 1.3 Global Energy Budget 3 1.4 TheWindow–Gray Approximation and the Greenhouse Effect 6 1.5 Climate Sensitivity and Climate Feedbacks 8 1.6 Radiative Time Constant 12 1.7 Composition of the Earth’s Atmosphere 14 1.8 Radiation and the Earth’s Mean Temperature Profile 19 1.9 The Spatial Distribution of Radiative Heating and Circulation 32 1.10 Summary and Outlook 35 References 39 2 Radiation and Its Sources 41 2.1 Light as an ElectromagneticWave 41 2.2 Radiation from an Oscillating Dipole, Radiance, and Radiative Flux 42 2.3 Radiometry 47 2.4 Blackbody Radiation: Light as a Photon 50 2.5 Incident Sunlight 57 References 63 3 Transfer of Radiation in the Earth’s Atmosphere 65 3.1 Cross Sections 65 3.2 Scattering Cross Section and Scattering Phase Function 68 3.3 Elementary Principles of Light Scattering 71 3.4 Equation of Radiative Transfer 77 3.5 Radiative Transfer Equations for Solar and Terrestrial Radiation 80 References 82 4 Solutions to the Equation of Radiative Transfer 85 4.1 Introduction 85 4.2 Formal Solution to the Equation of Radiative Transfer 86 4.3 Solution for Thermal Emission 88 4.4 Infrared Fluxes and Heating Rates 93 4.5 Formal Solution for Scattering and Absorption 102 4.6 Single Scattering Approximation 103 4.7 Fourier Decomposition of the Radiative Transfer Equation 110 4.8 The Legendre Series Representation and the Eddington Approximation 112 4.9 Adding Layers in the Eddington Approximation 121 4.10 Adding a Surface with a Nonzero Albedo in the Eddington Approximation 123 4.11 Clouds in theThermal Infrared 124 4.12 Optional Separation of Direct and Diffuse Radiances 126 4.13 Optional Separating the Diffusely Scattered Light from the Direct Beam in the Eddington and Two–Stream Approximations 127 4.14 Optional The –Eddington Approximation 130 4.15 Optional The Discrete OrdinateMethod and DISORT 135 4.16 Optional Adding–DoublingMethod 138 4.17 Optional Monte Carlo Simulations 140 References 146 5 Treatment of Molecular Absorption in the Atmosphere 149 5.1 Spectrally Averaged Transmissions 149 5.2 Molecular Absorption Spectra 151 5.3 Positions and Strengths of Absorption Lines within Vibration–Rotation Bands 155 5.4 Shapes of Absorption Lines 159 5.5 Doppler Broadening and the Voigt Line Shape 162 5.6 Average Absorptivity for a Single, Weak Absorption Line 163 5.7 Average Absorptivity for a Single, Strong, Pressure–Broadened Absorption Line 164 5.8 Treatment of Inhomogeneous Atmospheric Paths 166 5.9 Average Transmissivities for Bands of Nonoverlapping Absorption Lines 169 5.10 Approximate Treatments of Average Transmissivities for Overlapping Lines 171 5.11 Exponential Sum–Fit and Correlated k–Distribution Methods 177 5.12 Treatment of Overlapping Molecular Absorption Bands 182 References 184 6 Absorption of Solar Radiation by the Earth’s Atmosphere and Surface 185 6.1 Introduction 185 6.2 Absorption of UV and Visible Sunlight by Ozone 186 6.3 Absorption of Sunlight byWater Vapor 191 References 201 7 Simplified Estimates of Emission 203 7.1 Introduction 203 7.2 Emission in the 15 μmBand of CO2 203 7.3 Change in Emitted Flux due to Doubling of CO2 209 7.4 Changes in Stratospheric Emission and Temperature Caused by a Doubling of CO2 213 7.5 Afterthoughts 215 References 217 Appendix A Useful Physical and Geophysical Constants 219 Appendix B Solving Differential Equations 221 B.1 Simple Integration 221 B.2 Integration Factor 221 B.3 Second Order Differential Equations 223 Appendix C Integrals of the Planck Function 225 Appendix D RandomModel Summations of Absorption Line Parameters for the Infrared Bands of Carbon Dioxide 227 Reference 229 Appendix E Ultraviolet and Visible Absorption Cross Sections of Ozone 231 References 231 Index 233