Radiative Transfer in the Atmosphere and Ocean

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ISBN: 9780521890618 | 0521890616
Cover: Paperback
Copyright: 1/28/2002

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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.

List of Illustrations

xvii

Preface

xxi

Acknowledgments

xxv

Basic Properties of Radiation, Atmospheres, and Oceans

(33)

Introduction

(1)

Parts of the Spectrum

(5)

Extraterrestrial Solar Flux

(1)

Terrestrial Infrared Flux

(2)

Radiative Interaction with Planetary Media

(1)

Feedback Processes

(1)

Types of Matter that Affect Radiation

(1)

Vertical Structure of Planetary Atmospheres

(17)

Hydrostatic and Ideal Gas Laws

(4)

Minor Species in the Atmosphere

(1)

Optical Line-of-Sight Paths

(4)

Radiative Equilibrium and the Thermal Structure of Atmospheres

(3)

Climate Change: Radiative Forcing and Feedbacks

(4)

Density Structure of the Ocean

(1)

Vertical Structure of the Ocean

(4)

The Mixed Layer and the Deep Ocean

(1)

Seasonal Variations of Ocean Properties

(1)

Sea-Surface Temperature

(1)

Ocean Spectral Reflectance and Opacity

(1)

Remarks on Nomenclautre, Notation, and Units

(2)

Summary

(3)

Basic State Variables and the Radiative Transfer Equation

(22)

Introduction

(1)

Geometrical Optics

(1)

Radiative Flux or Irradiance

(2)

Spectral Intensity and Its Angular Moments

(4)

Relationship between Flux and Intensity

(1)

Average Intensity and Energy Density

(2)

Some Theorems on Intensity

(3)

Intensity and Flux from an Extended Source

(1)

Perception of Brightness: Analogy with Radiance

(1)

The Extinction Law

(5)

Extinction = Scattering + Absorption

(2)

The Differential Equation of Radiative Transfer

(2)

Summary

(3)

Basic Scattering Processes

(28)

Introduction

(2)

Lorentz Theory for Radiation-Matter Interactions

(6)

Scattering and Collective Effects in a Uniform Medium

(2)

Scattering from Density Irregularities

(1)

Scattering in Random Media

(1)

First-Order and Multiple Scattering

(1)

Scattering from a Damped Simple Harmonic Oscillator

(10)

Case (1): Resonance Scattering and the Lorentz Profile

(2)

Conservative and Nonconservative Scattering

(1)

Natural Broadening

(1)

Pressure Broadening

(1)

Doppler Broadening

(2)

Realistic Line-Broadening Processes

(1)

Case (2): Rayleigh Scattering

(2)

The Scattering Phase Function

(4)

Rayleigh-Scattering Phase Function

(3)

Mie-Debye Scattering

(1)

Summary

(5)

Absorption by Solid, Aqueous, and Gaseous Media

(46)

Introduction

(2)

Absorption on Surfaces, on Aerosols, and within Aqueous Media

(3)

Solids

(2)

Aerosols

(1)

Liquids

(1)

Molecular Absorption in Gases

(13)

Thermal Emission and Radiation Laws

(1)

Planck's Spectral Distribution Law

(4)

Radiative Excitation Processes in Molecules

(1)

Inelastic Collisional Processes

(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 III-Conditioning

299

(5)

Boundary Conditions

299

(3)

Removal of Numerical III-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 Elasser 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-Convenctive 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

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Radiative Transfer in the Atmosphere and Ocean

Summary

Table of Contents

Supplemental Materials