ALBERT

Description / Table of Contents: Contents: List of Illustrations. - Preface. - Acknowledgments. - 1 Basic Properties of Radiation, Atmospheres, and Oceans. - 1.1 lntroduction. - 1.2 Parts of the Spectrum. - 1.2.1 Extraterrestrial Solar Flux. - 1.2.2 Terrestrial lnfrared Flux. - 1.3 Radiative Interaction with Planetary Media. - 1.3.1 Feedback Processes. - 1.3.2 Types of Matter that Affect Radiation. - 1.4 Vertical Structure of Planetary Atmospheres. - 1.4.1 Hydrostatic and Ideal Gas Laws. - 1.4.2 Minor Species in the Atmosphere. - 1.4.3 Optical Line-of-Sight Paths. - 1.4.4 Radiative Equilibrium and the Thermal Structure of Atmospheres. - 1.4.5 Climate Change: Radiative Forcing and Feedbacks. - 1.5 Density Structure of the Ocean. - 1.6 Vertical Structure of the Ocean. - 1.6.1 The Mixed Layer and the Deep Ocean. - 1 .6.2 Seasonal Variations of Ocean Properties. - 1.6.3 Sea-Surface Temperature. - 1.6.4 Ocean Spectral Reflectance and Opacity. - 1.7 Remarks on Nomenclature, Notation, and Units. - 1.8 Summary. - 2 Basic State Variables and the Radiative Transfer Equation. - 2.1 Introduction.- 2.2 Geometrical Optics. - 2.3 Radiative Flux or Irradiance. - 2.4 Spectral Intensity and Its Angular Moments. - 2.4.1 Relationship between Flux and Intensity. - 2.4.2 Average Intensity and Energy Density. - 2.5 Some Theorems on Intensity. - 2.5.1 lntensity and Flux from an Extended Source. - 2.6 Perception of Brightness: Analogy with Radiance. - 2.7 The Extinction Law. - 2.7.1 Extinction = Scattering + Absorption. - 2.8 The Differential Equation of Radiative Transfer. - 2.9 Summary. - 3 Basic Scattering Processes. - 3.1 Introduction. - 3.2 Lorentz Theory for Radiation- Matter Interactions. - 3.2.1 Scattering and Collective Effects in a Uniform Medium. - 3.2.2 Scattering from Density Irregularities. - 3.2.3 Scattering in Random Media. - 3.2.4 First-Order and Multiple Scattering. - 3.3 Scattering from a Damped Simple Harmonic Oscillator. - 3.3.1 Case ( 1 ): Resonance Scattering and the Lorentz Profile. - 3.3.2 Conservative and Nonconservative Scattering. - 3.3.3 Natural Broadening. - 3.3.4 Pressure Broadening. - 3.3.5 Doppler Broadening. - 3.3.6 Realistic Line-Broadening Processes. - 3.3.7 Case (2): Rayleigh Scattering. - 3.4 The Scattering Phase Function. - 3.4.1 Rayleigh-Scattering Phase Function. - 3.5 Mie-Debye Scattering. - 3.6 Summary. - 4 Absorption by Solid, Aqueous, and Gaseous Media. - 4.1 Introduction. - 4.2 Absorption on Surfaces, on Aerosols, and within Aqueous Media. - 4.2.1 Solids. - 4.2.2 Aerosols. - 4.2.3 Liquids. - 4.3 Molecular Absorption in Gases. - 4.3.1 Thermal Emission and Radiation Laws. - 4.3.2 Planck's Spectral Distribution Law. - 4.3.3 Radiative Excitation Processes in Molecules. - 4.3.4 Inelastic Collisional Processes. - 4.3.5 Maintenance of Thermal Equilibrium Distributions. - 4.4 The Two-Level Atom. - 4.4.1 Microscopic Radiative Transfer Equation. - 4.4.2 Effects of Collisions on State Populations. - 4.5 Absorption in Molecular Lines and Bands. - 4.5.1 Molecular Rotation: The Rigid Rotator. - 4.5.2 Molecular Vibration and Rotation: The Vibrating Rotator. - 4.5.3 Line Strengths. - 4.6 Absorption Processes in the UV/Visible. - 4.7 Summary. - 5 Principles of Radiative Transfer. - 5.1 Introduction. - 5.2 Boundary Properties of Planetary Media. - 5.2.1 Thermal Emission from a Surface. - 5.2.2 Absorption by a Surface. - 5.2.3 Kirchhoff's Law for Surfaces. - 5.2.4 Surface Reflection: The BRDF. - 5.2.5 Albedo for Collimated lncidence. - 5.2.6 The Flux Reflectance, or Albedo: Diffuse Incidence. - 5.2.7 Analytic Reflectance Expressions. - 5.2.8 The Opposition Effect. - 5.2.9 Specular Reflection from the Sea Surface. - 5.2.10 Transmission through a Slab Medium. - 5.2.11 Spherical, or Bond Albedo. - 5.3 Absorption and Scattering in Planetary Media. - 5.3.1 Kirchhoff's Law for Volume Absorption and Emission. - 5.3.2 Differential Equation of Radiative Transfer. - 5.4 Solution of the Radiative Transfer Equation for Zero Scattering. - 5.4.1 Solution with Zero Scattering in Slab Geometry. - 5.4.2 Half-Range Quantities in a Slab Geometry. - 5.4.3 Formal Solution in a Slab Geometry. - 5.5 Gray Slab Medium in Local Thermodynamic Equilibrium. - 5.6 Formal Solution Including Scattering and Emission. - 5.7 Radiative Heating Rate. - 5.7.1 Generalized Gershun's Law. - 5.7.2 Warming Rate, or the Temperature Tendency. - 5.7.3 Actinic Radiation, Photolysis Rate, and Dose Rate. - 5.8 Summary. - 6 Formulation of Radiative Transfer Problems. - 6.1 Introduction. - 6.2 Separation into Diffuse and Direct (Solar) Components. - 6.2.1 Lower Boundary Conditions. - 6.2.2 Multiple Scattering. - 6.2.3 Azimuth lndependence of Flux and Mean Intensity. - 6.3 Azimuthal Dependence of the Radiation Field. - 6.4 Spherical Shell Geometry. - 6.5 Nonstratified Media. - 6.6 Radiative Transfer in the Atmosphere-Ocean System. - 6.6.1 Two Stratified Media with Different Indices of Refraction. - 6.7 Examples of Phase Functions. - 6.7.1 Rayleigh Phase Function. - 6.7.2 The Mie-Debye Phase Function. - 6.8 Scaling Transformations Useful for Anisotropic Scattering. - 6.8.1The [Delta]-Isotropic Approximation. - 6.8.2 The [Delta]- Two-Term Approximation. - 6.8.3 Remarks on Low-Order Scaling Approximations. - 6.8.4 The [Delta]-N Approximation: Arbitrary N. - 6.8.5 Mathematical and Physical Meaning of the Scaling. - 6.9 Prototype Problems in Radiative Transfer Theory. - 6.9.1 Prototype Problem 1: Uniform Illumination. - 6.9.2 Prototype Problem 2: Constant lmbedded Source. - 6.9.3 Prototype Problem 3: Diffuse Reflection Problem. - 6.9.4 Boundary Conditions: Reflecting and Emitting Surface. - 6.10 Reciprocity, Duality, and Inhomogeneaus Media. - 6.11 Effects of Surface Reflection on the Radiation Field. - 6.12 Integral Equation Formulation of Radiative Transfer. - 6.13 Probabilistic Aspects of Radiative Transfer. - 6.13.1 The Escape Probability. - 6.14 Summary. - 7 Approximate Salutions of Prototype Problems. - 7.1 Introduction. - 7.2 Separation of the Radiation Field into Orders of Scattering. - 7.2.1 Lambda Iteration: The Multiple-Scaltering Series. - 7.2.2 Single-Scattered Contribution from Ground Reflection: The Planetary Problem. - 7.3 The Two-Stream Approximation: Isotropic Scattering. - 7.3.1 Approximate Differential Equations. - 7.3.2 The Mean lnclination: Possible Choices for [My]. - 7.3.3 Prototype Problem 1: Differential-Equation Approach. - 7.3.4 Prototype Problem 2: lmbedded Source. - 7.3.5 Prototype Problem 3: Beam Incidence. - 7.4 Conservative Scattering in a Finite Slab. - 7.5 Anisotropic Scattering. - 7.5.1 Two-Stream Versus Eddington Approximations. - 7.5.2 The Backscattering Coefficients. - 7.5.3 Two-Stream Salutions for Anisotropic Scattering. - 7.5.4 Scaling Approximations for Anisotropic Scattering. - 7.5.5 Generalized Two-Stream Equations. - 7.6 Accuracy of the Two-Stream Method. - 7.7 Final Comments on the Two-Stream Method. - 7.8 Summary. - 8 Accurate Numerical Salutions of Prototype Problems. - 8.1 Introduction. - 8.2 Discrete-Ordinate Method - Isotropic Scattering. - 8.2.1 Quadrature Formulas. - 8.2.2 The Double-Gauss Method. - 8.3 Anisotropic Scattering. - 8.3.1 General Considerations. - 8.3.2 Quadrature Rule. - 8.4 Matrix Formulation of the Discrete-Ordinate Method. - 8.4.1 Two- and Four-Stream Approximations. - 8.4.2 Multistream Approximation ( N Arbitrary). - 8.5 Matrix Eigensolutions. - 8.5.1 Two-Stream Salutions ( N = 1). - 8.5.2 Multistream Solutions ( N Arbitrary). - 8.5.3 Inhomogeneous Solution. - 8.5.4 General Solution. - 8.6 Source Function and Angular Distributions. - 8.7 Boundary Conditions - Removal of Ill-Conditioning. - 8.7.1 Boundary Conditions. - 8.7.2 Removal of Numerical lll-Conditioning. - 8.8 Inhomogeneous Multilayered Media. - 8.8.1 General Solution - Boundary and Layer Interface Conditions. - 8.8.2 Source Functions and Angular Distributions. - 8.8.3 Numerical lmplementation of the Discrete-Ordinate Method. - 8.9 Correction of the Truncated Intensity Field. - 8.9.1 The Nakajima-Tanaka Correction Procedure. - 8.9.2 Computed lntensity Distributions for the Standard Problem. - 8.10 The Coupled Atmosphere-Ocean Problem. - 8.10.1 Discretized Equations for the Atmosphere-Ocean System. - 8.10.2 Quadrature and General Solution. - 8.10.3 Boundary, Continuity, and Atmosphere-Ocean Interface Conditions. - 8.11 The Doubling-Adding and the Matrix Operator Methods. - 8.11.1 Matrix-Exponential Solution - Formal Derivation of Doubling Rules. - 8.11.2 Connection between Doubling and Discrete-Ordinate Methods. - 8.11.3 Intuitive Derivation of the Doubling Rules - Adding of Dissimilar Layers. - 8.12 Other Accurate Methods. - 8.12.1 The Spherical-Harmonics Method. - 8.12.2 Invariant lmbedding. - 8.12.3 Iteration Methods. - 8.12.4 The Feautrier Method. - 8.12.5 Integral Equation Approach. - 8.12.6 Monte Carlo Methods. - 8.13 Summary. - 9 Shortwave Radiative Transfer. - 9.1 Introduction. - 9.2 Solar Radiation. - 9.3 Optical Properties of the Earth-Atmosphere System. - 9.3.1 Gaseaus Absorption and Penetration Depth. - 9.3.2 Optical Properlies of Atmospheric Aerosols. - 9.3.3 Optical Properties of Warm (Liquid Water) Clouds. - 9.3.4 Optical Properties of Ice Clouds. - 9.3.5 Optical Properties of the Ocean. - 9.3.6 Optical Properties of Snow and Ice. - 9.4 Modeling of Shortwave Radiative Effects in the Atmosphere. - 9.4.1 Spectral Averaging Procedure: The Chandrasekhar Mean. - 9.4.2 Solar Warming Rates Due to Ozone, Aerosols, and Clouds. - 9.4.3 Computation of Photolysis Rates. - 9.4.4 UV Transmission: Relation to Ozone Abundance. - 9.4.5 UV Transmission and Dose Rates at the Earth 's Surface. - 9.4.6 Comparisan of Measured and Computed UV Irradiance at the Surface. - 9.5 Modeling of Shortwave Radiation in the Ocean. - 9.5.1 Diffuse Radiation: Attenuation in the Ocean. - 9.5.2 Two-Stream Model Appropriate for Deep Water. - 9.5.3 Backscattering by Ocean Particles: The Role of Shape Factars. - 9.5.4 Approximate Expressions for the Remotely Sensed Reflectance. - 9.5.5 Modefing the UV Transmission into the Ocean. - 9.5.6 Measured and Computed UV Irradiance in the Ocean. - 9.6 Interaction of Solar Radiation with Snow and Ice. - 9.7 Summary. - 1 0 Transmission in Spectrally Complex Media. - 10.1 Introduction. - 10.2 Transmission in an Isolated Line. - 10.2.1 Isolated Lorentz Line. - 10.3 Band Models. - 10.3.1 The Elsasser Band Model. - 10.3.2 Distributed Line lntensities. - 10.3.3 Random Band Model. - 10.3.4 MODTRAN: A Moderate-Resolution Band Model. - 10.4 Spectral Mapping Transformations for Homogeneous Media. - 10.4.1 Method of the k-Distribution. - 10.4.2 k-Distribution for the Malkmus Band Model. - 10.5 Transmission in Nongray Inhomogeneaus Media. - 10.5.1 The H- C-G Scaling Approximation. - 10.5.2 LBL Transmission Computation: Inhomogeneaus Paths. - 10.5.3 Inclusion of Multiple Scattering in LBL Computations. - 10.5.4 The Correlated-k Method. - 10.5.5 Inclusion of Multiple Scattering in the Correlated-k Method. - 10.6 Summary. - 11 Radiative Transfer in Nongray Media. - 11.1 lntroduction. - 11.2 Radiative Flux and Heating Rate: Clear-Sky Conditions. - 11.2.1 Monochromatic Flux Equations. - 11.2.2 Wide-Band Emittance Models. - 11.2.3 Narrow-Band Absorption Model. - 11.2.4 Band Overlap. - 11.2.5 The Diffusivity Approximation. - 11.2.6 Equationsfor the Heating Rate. - 11.2.7 Clear-Sky Radiative Cooling: Nonisothermal Medium. - 11.2.8 Computations of Terrestrial Cooling Rates. - 11.3 The IR Radiative Impact of Clouds and Aerosols. - 11.3.1Heating Rate in an Idealized Cloud. - 11.3.2 Detailed Longwave Radiative Effects of Clouds. - 11.3.3 Accurate Treatment Including Scattering. - 11.4 Summary. - 12 The Role of Radiation in Climate. - 12.1 Introduction. - 12.2 Radiative Equilibrium with Zero Visible Opacity. - 12.3 Radiative Equilibrium with Finite Visible Opacity. - 12.4 Radiative-Convective Equilibrium. - 12.5 The Concept of the Emission Height. - 12.6 Effects of spectral window. - 12.7 Radiative forcing. - 12.8 Climate impact of clouds. - 12.8.1 Longwave Effects of water clouds. - 12.8.2 Shortwave effects of water clouds. - 12.8.3 Combined shortwave and longewave effects of clouds. - 12.9 Climate impact of cloud height. - 12.10 Cloud and aerosol forcing. - 12.10.1 Aerosol forcing. - 12.11 Water-Vapor Feedback. - 12.12 Effects of carbon dioxide changes. - 12.13 Greenhouse effect from individual gas species. - 12.14 Summary. - Appendices. - A Nomenclature: Glossary of symbols. - B Physical constants. - C Model atmospheres. - D Ocean optics nomenclature. - E Reflectance and transmittance at an interface. - Index.

Description / Table of Contents: Radiative transfer is important to a range of disciplines, from the study of greenhause warming to stellar atmospheres and ocean optics. This text provides a foundation of the theoretical and practical aspects of radiative transfer for senior undergraduate and graduate students of atmospheric, oceanic, and environmental sciences. With an emphasis on formulation, judicial approximations and numerical solutions of the radiative transfer equation, Radiative Transfer in the Atmosphere and Ocean fills a gap between descriptive texts covering the physical processes and the practical numerical approaches needed in research. Designed to convey physical insight into the transfer process, it can also be used as a self-contained manual for practitioners who require accurate modeling of the effects of solar and infrared radiation on natural systems. Radiative Transfer in the Atmosphere and Ocean includes a unified treatment of radiation within both the atmosphere and ocean, boundary properties (such as reflectionand absorptance of solid surfaces), heuristic models (Lorentzatom, two-level atom, rotating vibrator), and extensive use of two-stream and approximate methods. State of the-art computational methods are illustrated by a thorough treatment of the discrete-ordinates technique and the correlated-k band absorption method. Exercises and problem sets provide practice in both formulation and solution techniques. Applications to the subjects of solar UV penetration of the atmosphere / ocean system and the greenhause effect serve to illustrate the use of such techniques in modern research. This self-contained, systematic treatment will prepare the student in solving radiative transfer problems across a broad range of subjects.