Radiative Transfer in the Atmosphere and Ocean

by Gary E. Thomas , Knut Stamnes

• ISBN13: 9780521401241
• ISBN10: 0521401240
• Format: Hardcover
• Copyright: 1999-08-13
• Publisher: Cambridge University Press

Summary

This text provides a foundation in both the theoretical and practical aspects of radiative transfer, for advanced students of atmospheric, oceanic and environmental sciences. The transfer of solar and infrared radiation through optically-thick clouds, aerosol layer, and the oceanic mixed layer is presented through the use of heuristic models of scattering and absorption, and a systematic approach to formulation and solution of the radiative transfer equation. Problems such as the the transmission of ultraviolet radiation through the atmosphere and ocean, remote sensing, solar heating and infrared cooling processes, UV biological dose rates, and Greenhouse warming are solved using a variety of methods. This self-contained, systematic treatment will prepare students from a range of disciplines in problems concerning the effects of solar and infrared radiation on natural systems. The hardback edition received excellent reviews.

Table of Contents

List of Illustrations	xvii
Preface	xxi
Acknowledgments	xxv
Basic Properties of Radiation, Atmospheres, and Oceans	1	(33)
Introduction	1	(1)
Parts of the Spectrum	1	(5)
Extraterrestrial Solar Flux	3	(1)
Terrestrial Infrared Flux	4	(2)
Radiative Interaction with Planetary Media	6	(1)
Feedback Processes	6	(1)
Types of Matter that Affect Radiation	6	(1)
Vertical Structure of Planetary Atmospheres	7	(17)
Hydrostatic and Ideal Gas Laws	8	(4)
Minor Species in the Atmosphere	12	(1)
Optical Line-of-Sight Paths	13	(4)
Radiative Equilibrium and the Thermal Structure of Atmospheres	17	(3)
Climate Change: Radiative Forcing and Feedbacks	20	(4)
Density Structure of the Ocean	24	(1)
Vertical Structure of the Ocean	25	(4)
The Mixed Layer and the Deep Ocean	25	(1)
Seasonal Variations of Ocean Properties	26	(1)
Sea-Surface Temperature	27	(1)
Ocean Spectral Reflectance and Opacity	28	(1)
Remarks on Nomenclature, Notation, and Units	29	(2)
Summary	31	(3)
Basic State Variables and the Radiative Transfer Equation	34	(22)
Introduction	34	(1)
Geometrical Optics	35	(1)
Radiative Flux or Irradiance	36	(2)
Spectral Intensity and Its Angular Moments	38	(4)
Relationship between Flux and Intensity	39	(1)
Average Intensity and Energy Density	40	(2)
Some Theorems on Intensity	42	(3)
Intensity and Flux from an Extended Source	44	(1)
Perception of Brightness: Analogy with Radiance	45	(1)
The Extinction Law	46	(5)
Extinction = Scattering + Absorption	49	(2)
The Differential Equation of Radiative Transfer	51	(2)
Summary	53	(3)
Basic Scattering Processes	56	(28)
Introduction	56	(2)
Lorentz Theory for Radiation-Matter Interactions	58	(6)
Scattering and Collective Effects in a Uniform Medium	59	(2)
Scattering from Density Irregularities	61	(1)
Scattering in Random Media	62	(1)
First-Order and Multiple Scattering	63	(1)
Scattering from a Damped Simple Harmonic Oscillator	64	(10)
Case (1): Resonance Scattering and the Lorentz Profile	65	(2)
Conservative and Nonconservative Scattering	67	(1)
Natural Broadening	68	(1)
Pressure Broadening	69	(1)
Doppler Broadening	70	(2)
Realistic Line-Broadening Processes	72	(1)
Case (2): Rayleigh Scattering	72	(2)
The Scattering Phase Function	74	(4)
Rayleigh-Scattering Phase Function	75	(3)
Mie--Debye Scattering	78	(1)
Summary	79	(5)
Absorption by Solid, Aqueous, and Gaseous Media	84	(46)
Introduction	84	(2)
Absorption on Surfaces, on Aerosols, and within Aqueous Media	86	(3)
Solids	86	(2)
Aerosols	88	(1)
Liquids	88	(1)
Molecular Absorption in Gases	89	(13)
Thermal Emission and Radiation Laws	93	(1)
Planck's Spectral Distribution Law	93	(4)
Radiative Excitation Processes in Molecules	97	(1)
Inelastic Collisional Processes	98	(3)
Maintenance of Thermal Equilibrium Distributions	101	(1)
The Two-Level Atom	102	(8)
Microscopic Radiative Transfer Equation	102	(5)
Effects of Collisions on State Populations	107	(3)
Absorption in Molecular Lines and Bands	110	(12)
Molecular Rotation: The Rigid Rotator	114	(1)
Molecular Vibration and Rotation: The Vibrating Rotator	115	(3)
Line Strengths	118	(4)
Absorption Processes in the UV/Visible	122	(3)
Summary	125	(5)
Principles of Radiative Transfer	130	(40)
Introduction	130	(1)
Boundary Properties of Planetary Media	131	(17)
Thermal Emission from a Surface	131	(1)
Absorption by a Surface	132	(1)
Kirchhoff's Law for Surfaces	133	(1)
Surface Reflection: The BRDF	134	(4)
Albedo for Collimated Incidence	138	(1)
The Flux Reflectance, or Albedo: Diffuse Incidence	138	(2)
Analytic Reflectance Expressions	140	(2)
The Opposition Effect	142	(1)
Specular Reflection from the Sea Surface	143	(2)
Transmission through a Slab Medium	145	(1)
Spherical, or Bond Albedo	146	(2)
Absorption and Scattering in Planetary Media	148	(3)
Kirchhoff's Law for Volume Absorption and Emission	148	(2)
Differential Equation of Radiative Transfer	150	(1)
Solution of the Radiative Transfer Equation for Zero Scattering	151	(7)
Solution with Zero Scattering in Slab Geometry	154	(1)
Half-Range Quantities in a Slab Geometry	155	(1)
Formal Solution in a Slab Geometry	156	(2)
Gray Slab Medium in Local Thermodynamic Equilibrium	158	(1)
Formal Solution Including Scattering and Emission	159	(2)
Radiative Heating Rate	161	(4)
Generalized Gershun's Law	162	(1)
Warming Rate, or the Temperature Tendency	163	(1)
Actinic Radiation, Photolysis Rate, and Dose Rate	164	(1)
Summary	165	(5)
Formulation of Radiative Transfer Problems	170	(47)
Introduction	170	(1)
Separation into Diffuse and Direct (Solar) Components	170	(7)
Lower Boundary Conditions	173	(1)
Multiple Scattering	174	(1)
Azimuth Independence of Flux and Mean Intensity	175	(2)
Azimuthal Dependence of the Radiation Field	177	(4)
Spherical Shell Geometry	181	(2)
Nonstratified Media	183	(1)
Radiative Transfer in the Atmosphere-Ocean System	184	(3)
Two Stratified Media with Different Indices of Refraction	185	(2)
Examples of Phase Functions	187	(3)
Rayleigh Phase Function	187	(1)
The Mie--Debye Phase Function	188	(2)
Scaling Transformations Useful for Anisotropic Scattering	190	(7)
The δ-Isotropic Approximation	192	(1)
The δ-Two-Term Approximation	193	(1)
Remarks on Low-Order Scaling Approximations	194	(1)
The δ-N Approximation: Arbitrary N	194	(2)
Mathematical and Physical Meaning of the Scaling	196	(1)
Prototype Problems in Radiative Transfer Theory	197	(5)
Prototype Problem 1: Uniform Illumination	197	(1)
Prototype Problem 2: Constant Imbedded Source	198	(1)
Prototype Problem 3: Diffuse Reflection Problem	199	(1)
Boundary Conditions: Reflecting and Emitting Surface	199	(3)
Reciprocity, Duality, and Inhomogeneous Media	202	(1)
Effects of Surface Reflection on the Radiation Field	203	(2)
Integral Equation Formulation of Radiative Transfer	205	(2)
Probabilistic Aspects of Radiative Transfer	207	(4)
The Escape Probability	210	(1)
Summary	211	(6)
Approximate Solutions of Prototype Problems	217	(64)
Introduction	217	(1)
Separation of the Radiation Field into Orders of Scattering	218	(7)
Lambda Iteration: The Multiple-Scattering Series	220	(4)
Single-Scattered Contribution from Ground Reflection: The Planetary Problem	224	(1)
The Two-Stream Approximation: Isotropic Scattering	225	(22)
Approximate Differential Equations	225	(2)
The Mean Inclination: Possible Choices for μ	227	(1)
Prototype Problem 1: Differential-Equation Approach	227	(10)
Prototype Problem 2: Imbedded Source	237	(5)
Prototype Problem 3: Beam Incidence	242	(5)
Conservative Scattering in a Finite Slab	247	(1)
Anisotropic Scattering	248	(15)
Two-Stream Versus Eddington Approximations	248	(5)
The Backscattering Coefficients	253	(5)
Two-Stream Solutions for Anisotropic Scattering	258	(2)
Scaling Approximations for Anisotropic Scattering	260	(1)
Generalized Two-Stream Equations	261	(2)
Accuracy of the Two-Stream Method	263	(4)
Final Comments on the Two-Stream Method	267	(2)
Summary	269	(12)
Accurate Numerical Solutions of Prototype Problems	281	(54)
Introduction	281	(1)
Discrete-Ordinate Method -- Isotropic Scattering	281	(6)
Quadrature Formulas	281	(3)
The Double-Gauss Method	284	(3)
Anisotropic Scattering	287	(2)
General Considerations	287	(2)
Quadrature Rule	289	(1)
Matrix Formulation of the Discrete-Ordinate Method	289	(4)
Two- and Four-Stream Approximations	289	(3)
Multistream Approximation (N Arbitrary)	292	(1)
Matrix Eigensolutions	293	(4)
Two-Stream Solutions (N = 1)	293	(1)
Multistream Solutions (N Arbitrary)	294	(1)
Inhomogeneous Solution	295	(1)
General Solution	296	(1)
Source Function and Angular Distributions	297	(2)
Boundary Conditions -- Removal of Ill-Conditioning	299	(5)
Boundary Conditions	299	(3)
Removal of Numerical Ill-Conditioning	302	(2)
Inhomogeneous Multilayered Media	304	(5)
General Solution -- Boundary and Layer Interface Conditions	304	(2)
Source Functions and Angular Distributions	306	(1)
Numerical Implementation of the Discrete-Ordinate Method	307	(2)
Correction of the Truncated Intensity Field	309	(6)
The Nakajima--Tanaka Correction Procedure	309	(3)
Computed Intensity Distributions for the Standard Problem	312	(3)
The Coupled Atmosphere--Ocean Problem	315	(5)
Discretized Equations for the Atmosphere--Ocean System	315	(1)
Quadrature and General Solution	316	(2)
Boundary, Continuity, and Atmosphere--Ocean Interface Conditions	318	(2)
The Doubling-Adding and the Matrix Operator Methods	320	(6)
Matrix-Exponential Solution -- Formal Derivation of Doubling Rules	323	(1)
Connection between Doubling and Discrete-Ordinate Methods	324	(1)
Intuitive Derivation of the Doubling Rules -- Adding of Dissimilar Layers	324	(2)
Other Accurate Methods	326	(2)
The Spherical-Harmonics Method	326	(1)
Invariant Imbedding	327	(1)
Iteration Methods	327	(1)
The Feautrier Method	328	(1)
Integral Equation Approach	328	(1)
Monte Carlo Methods	328	(1)
Summary	328	(7)
Shortwave Radiative Transfer	335	(49)
Introduction	335	(1)
Solar Radiation	336	(1)
Optical Properties of the Earth--Atmosphere System	337	(14)
Gaseous Absorption and Penetration Depth	337	(3)
Optical Properties of Atmospheric Aerosols	340	(2)
Optical Properties of Warm (Liquid Water) Clouds	342	(1)
Optical Properties of Ice Clouds	343	(4)
Optical Properties of the Ocean	347	(1)
Optical Properties of Snow and Ice	348	(3)
Modeling of Shortwave Radiative Effects in the Atmosphere	351	(11)
Spectral Averaging Procedure: The Chandrasekhar Mean	353	(1)
Solar Warming Rates Due to Ozone, Aerosols, and Clouds	353	(2)
Computation of Photolysis Rates	355	(1)
UV Transmission: Relation to Ozone Abundance	356	(1)
UV Transmission and Dose Rates at the Earth's Surface	357	(4)
Comparison of Measured and Computed UV Irradiance at the Surface	361	(1)
Modeling of Shortwave Radiation in the Ocean	362	(8)
Diffuse Radiation: Attenuation in the Ocean	362	(1)
Two-Stream Model Appropriate for Deep Water	363	(1)
Backscattering by Ocean Particles: The Role of Shape Factors	364	(3)
Approximate Expressions for the Remotely Sensed Reflectance	367	(1)
Modeling the UV Transmission into the Ocean	368	(1)
Measured and Computed UV Irradiance in the Ocean	369	(1)
Interaction of Solar Radiation with Snow and Ice	370	(2)
Summary	372	(12)
Transmission in Spectrally Complex Media	384	(29)
Introduction	384	(1)
Transmission in an Isolated Line	385	(3)
Isolated Lorentz Line	387	(1)
Band Models	388	(6)
The Elsasser Band Model	388	(1)
Distributed Line Intensities	389	(2)
Random Band Model	391	(1)
MODTRAN: A Moderate-Resolution Band Model	392	(2)
Spectral Mapping Transformations for Homogeneous Media	394	(5)
Method of the k-Distribution	395	(4)
k-Distribution for the Malkmus Band Model	399	(1)
Transmission in Nongray Inhomogeneous Media	399	(10)
The H--C--G Scaling Approximation	400	(1)
LBL Transmission Computation: Inhomogeneous Paths	401	(1)
Inclusion of Multiple Scattering in LBL Computations	402	(2)
The Correlated-k Method	404	(4)
Inclusion of Multiple Scattering in the Correlated-k Method	408	(1)
Summary	409	(4)
Radiative Transfer in Nongray Media	413	(25)
Introduction	413	(1)
Radiative Flux and Heating Rate: Clear-Sky Conditions	414	(14)
Monochromatic Flux Equations	415	(2)
Wide-Band Emittance Models	417	(4)
Narrow-Band Absorption Model	421	(1)
Band Overlap	422	(1)
The Diffusivity Approximation	422	(1)
Equations for the Heating Rate	423	(2)
Clear-Sky Radiative Cooling: Nonisothermal Medium	425	(2)
Computations of Terrestrial Cooling Rates	427	(1)
The IR Radiative Impact of Clouds and Aerosols	428	(6)
Heating Rate in an Idealized Cloud	428	(2)
Detailed Longwave Radiative Effects of Clouds	430	(2)
Accurate Treatment Including Scattering	432	(2)
Summary	434	(4)
The Role of Radiation in Climate	438	(73)
Introduction	438	(2)
Radiative Equilibrium with Zero Visible Opacity	440	(7)
Radiative Equilibrium with Finite Visible Opacity	447	(3)
Radiative--Convective Equilibrium	450	(3)
The Concept of the Emission Height	453	(1)
Effects of a Spectral Window	454	(2)
Radiative Forcing	456	(2)
Climate Impact of Clouds	458	(7)
Longwave Effects of Water Clouds	459	(2)
Shortwave Effects of Water Clouds	461	(3)
Combined Shortwave and Longwave Effects of Clouds	464	(1)
Climate Impact of Cloud Height	465	(2)
Cloud and Aerosol Forcing	467	(4)
Aerosol Forcing	470	(1)
Water-Vapor Feedback	471	(1)
Effects of Carbon Dioxide Changes	472	(1)
Greenhouse Effect from Individual Gas Species	473	(1)
Summary	474	(7)
Appendices
A Nomenclature: Glossary of Symbols	481	(8)
B Physical Constants	489	(1)
C Model Atmospheres	490	(13)
D Ocean Optics Nomenclature	503	(3)
E Reflectance and Transmittance at an Interface	506	(5)
Index	511