Rotational Raman scattering in the Earth's atmosphere ... - SRON

Contents
1 Introduction 1
1.1 Observing skylight 1
1.2 The Ring effect: a short historical background 3
1.3 The Ring effect: elastic and inelastic light scattering by air molecules 6
1.3.1 Energy states of N 2 and O 2 molecules 6
1.3.2 Elastic and inelastic scattering by air molecules 7
1.4 Accurate simulation of reflectivity spectra 12
1.4.1 Polarization aspects of light 12
1.4.2 Inclusion of inelastic scattering in radiative transfer modeling 14
1.4.3 Current status 14
1.5 Scope of this thesis 15
2 A doubling-adding method to include multiple orders of rotational Raman scattering 17
2.1 Introduction 17
2.2 The adding method including inelastic scattering 19
2.3 Numerical implementation 22
2.3.1 Discretization 22
2.3.2 Trade-off between accuracy and computational effort 25
2.4 Simulation of multiple inelastic scattering in the Earth’s atmosphere 29
2.5 Compensating for the neglect of multiple inelastic Raman scattering 31
2.6 Summary 35
2.A Appendix: Optical properties of Rayleigh, Cabannes and Raman scattering 36
3 A vector radiative transfer model using the perturbation theory approach 39
3.1 Introduction 39
3.2 The radiative transfer problem 42
3.2.1 The radiative transfer equation including both elastic Cabannes scattering and
inelastic Raman scattering 42
3.2.2 Decomposition of the radiative transfer problem 45
3.3 Perturbation Theory 46
3.3.1 The perturbation series approach 46
3.3.2 The adjoint transport problem 49