Radiation in the atmosphere : a course in theoretical meteorology

Preface page x 1 Introduction 1 1.1 The atmospheric radiation field 1 1.2 The mean global radiation budget of the Earth 3 1.3 Solar–terrestrial relations 8 1.4 Basic definitions of radiative quantities 16 1.5 The net radiative flux density vector 21 1.6 The interaction of radiation with matter 23 1.7 Problems 26 2 The radiative transfer equation 28 2.1 Eulerian derivation of the radiative transfer equation 28 2.2 The direct–diffuse splitting of the radiance field 34 2.3 The radiatively induced temperature change 36 2.4 The radiative transfer equation for a horizontally homogeneous atmosphere 37 2.5 Splitting of the radiance field into upwelling and downwelling radiation 46 2.6 The solution of the radiative transfer equation for a horizontally homogeneous atmosphere 51 2.7 Radiative flux densities and heating rates 57 2.8 Appendix 61 2.9 Problems 62 3 Principles of invariance 64 3.1 Definitions of the scattering and transmission functions 64 3.2 Diffuse reflection in a semi-infinite atmosphere 66 3.3 Chandrasekhar’s four statements of the principles of invariance 70 3.4 The inclusion of surface reflection 75 vii viii Contents 3.5 Diffuse reflection and transmission for isotropic scattering 78 3.6 Problems 80 4 Quasi-exact solution methods for the radiative transfer equation 82 4.1 The matrix operator method 82 4.2 The successive order of scattering method 92 4.3 The discrete ordinate method 95 4.4 The spherical harmonics method 104 4.5 The finite difference method 110 4.6 The Monte Carlo method 118 4.7 Appendix 128 4.8 Problems 131 5 Radiative perturbation theory 133 5.1 Adjoint formulation of the radiative transfer equation 133 5.2 Boundary conditions 137 5.3 Radiative effects 143 5.4 Perturbation theory for radiative effects 147 5.5 Appendix 153 5.6 Problems 157 6 Two-stream methods for the solution of the radiative transfer equation 158 6.1 ن-scaling of the phase function 158 6.2 The two-stream radiative transfer equation 161 6.3 Different versions of two-stream methods 166 6.4 Analytical solution of the two-stream methods for a homogeneous layer 172 6.5 Approximate treatment of scattering in the infrared spectral region 176 6.6 Approximations for partial cloud cover 179 6.7 The classical emissivity approximation 183 6.8 Radiation charts 190 6.9 Radiative equilibrium 195 6.10 Problems 201 7 Transmission in individual spectral lines and in bands of lines 204 7.1 The shape of single spectral lines 205 7.2 Band models 216 7.3 The fitting of transmission functions 237 7.4 Transmission in inhomogeneous atmospheres 255 7.5 Results 261 7.6 Appendix 265 7.7 Problems 271 8 Absorption by gases 276 8.1 Introduction 276 Contents ix 8.2 Molecular vibrations 277 8.3 Some basic principles from quantum mechanics 288 8.4 Vibrations and rotations of molecules 304 8.5 Matrix elements, selection rules and line intensities 316 8.6 Influence of thermal distribution of quantum states on line intensities 320 8.7 Rotational energy levels of polyatomic molecules 322 8.8 Appendix 327 8.9 Problems 332 9 Light scattering theory for spheres 333 9.1 Introduction 333 9.2 Maxwell’s equations 334 9.3 Boundary conditions 336 9.4 The solution of the wave equation 339 9.5 Mie’s scattering problem 345 9.6 Material characteristics and derived directional quantities 359 9.7 Selected results from Mie theory 367 9.8 Solar heating and infrared cooling rates in cloud layers 374 9.9 Problems 376 10 Effects of polarization in radiative transfer 378 10.1 Description of elliptic, linear and circular polarization 378 10.2 The Stokes parameters 383 10.3 The scattering matrix 386 10.4 The vector form of the radiative transfer equation 395 10.5 Problems 397 11 Remote sensing applications of radiative transfer 399 11.1 Introduction 399 11.2 Remote sensing based on short- and long-wave radiation 402 11.3 Inversion of the temperature profile 417 11.4 Radiative perturbation theory and ozone profile retrieval 431 11.5 Appendix 440 11.6 Problems 441 12 Influence of clouds on the climate of the Earth 443 12.1 Cloud forcing 443 12.2 Cloud feedback in climate models 446 12.3 Problems 451 Answers to problems 452 List of frequently used symbols 459 References 466 Index 478