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

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6 Chapter 1 In this thesis we focus on a passive remote sensing application. Here, not an artificial controllable monochromatic beam is used as the light source, but the Sun, which emits a continuous spectrum. The Raman effect is thus induced by N 2 and O 2 molecules at all these wavelengths. In this particular application of remote sensing of the Earth the Raman effect is referred to as the Ring effect. 1.3 The Ring effect: elastic and inelastic light scattering by air molecules 1.3.1 Energy states of N 2 and O 2 molecules To understand the energy exchange between N 2 and O 2 molecules and light that causes the Ring effect we need to consider the energy states of N 2 and O 2 molecules first. Molecular energy states can be grouped into: (1) electronic energy states, which are related to the orbital energy of the electrons, (2) vibrational energy states, which correspond to vibrations of the nuclei, and (3) rotational energy states, which are related to rotations of the nuclei around their center of mass (e.g. Rybicki and Lightman [1979], Bransden and Joachain [1996]). A transition from one state to another state involves a fixed energy difference. Electronic transitions involve energy differences of several eV, vibrational transitions involve energy differences in the order of 0.1 eV, and rotational transitions involve energy differences in the order of 0.001 eV. A key parameter that determines the population of the energy states of the molecules in a gas is the temperature of the gas. In the Earth’s atmosphere the temperature ranges from approximately 200 K to 300 K (e.g. Thomas and Stamnes [1999]). The population of energy states is described by the Maxwell-Boltzmann distribution. This distribution shows that the majority of the N 2 and O 2 molecules in the Earth’s atmosphere occupy the ground electronic-vibrational energy state and various rotational energy states belonging to this ground state. The spin states of the nuclei also influence the population of energy states of an ensemble of molecules. Using the Pauli exclusion principle it is found that the overall wave function of the homonuclear diatomic molecules N 2 and O 2 must be symmetric, and that only certain wave functions are acceptable when the two identical nuclei are exchanged (e.g. [Bransden and Joachain, 1996, Atkins and de Paula, 2002]). Knowing that the nuclei of the O 2 molecule are spin-0 particles and using symmetry considerations it follows that O 2 molecule in the ground electronic state can only exist for energy states that correspond to an odd total angular momentum quantum number J. In other words, even J energy states of O 2 do not occur. For N 2 the situation is different. The nuclei of the N 2 molecule are spin-1 particles. Using the same symmetry considerations it is found that both odd J and even J energy states occur, but that there are two times more N 2 molecules in the even J state than in the odd J state. The energy E of vibrating and rotating molecules such as N 2 and O 2 is given by E(v,J) = E vib (v) + E rot (v,J) (1.1) where E vib is the vibrational energy, v is the vibrational quantum number, and E rot is the rotational
Introduction 7 energy: E rot (v,J) = hcB v J(J+1) − hcD v J 2 (J+1) 2 . (1.2) Here, h is Plank’s constant, c is the speed of light in vacuum, B is the rotational constant, and D is the centrifugal distortion constant of the specific molecule. The first term in Eq. (1.2) describes how the rotational energy increases for increasing angular momentum (J). The second term corrects the energy levels for the stretching of the molecular bond due to the centrifugal force that acts on the nuclei in the rotating molecule. The values of B v and D v are characteristic for each molecular species and are given for the ground vibrational state (v = 0): B 0 = 1.99 cm −1 , D 0 = 5.76 × 10 −6 cm −1 for N 2 and B 0 = 1.44 cm −1 , D 0 = 4.85 × 10 −6 cm −1 for O 2 [Penney et al., 1974]. 1.3.2 Elastic and inelastic scattering by air molecules To describe the interaction between light and molecules we use the concept of photons. Scattering of light by molecules involves two steps. First, an incident photon brings a molecule to a virtual excited energy state by absorbing the energy of this photon. Then, the molecule falls back to a lower energy state by releasing a photon (see Fig. 1.3). The energy of a photon is E photon = hcν , (1.3) where ν =1/λ is the wavenumber. Here, E photon equals the energy difference of two molecular states. According to quantum theory each molecular transition process should obey the quantum law J →J ′ =J ± 1, where J is the total angular momentum quantum number of the initial state and J ′ is the quantum number of the final state of the absorbing molecule. Therefore, for a two step process, the net change in the total angular momentum quantum number becomes ∆J= −2, 0, +2. In addition, the vibrational energy of the molecule might change, i.e. ∆v= −1, 0, +1. Changes in rotational energy are allowed only if the molecule has an anisotropic polarizability. Changes in vibrational energy are allowed only when the polarizability of the molecule changes as the molecule swells and contracts [Long, 1977, Atkins and de Paula, 2002]. Both criteria hold for the N 2 and the O 2 molecule which means that in principle both vibrational and rotational Raman scattering need to be considered. Scattering processes that involve no net exchange of energy (∆J = 0; ∆v = 0) between the molecule and the photons correspond to elastic scattering, whereas scattering processes that involve an exchange of rotational and/or vibrational energy are inelastic. Elastic scattering by air molecules is referred to as Cabannes scattering (Fig. 1.3a). It is worth to mention that the specific naming of the various spectral components is not always that clear in the literature. In this thesis we adopt the terminology that was proposed by Young [1982]. The light that is inelastically scattered due to (rotational-)vibrational Raman scattering (∆v = +1; ∆J = 0, ±2) represents only a small fraction of the total inelastically scattered light, i.e. approximately 1/30th [Burrows et al., 1996]. Therefore, it is sufficient to consider pure rotational Raman scattering only (∆v = 0; ∆J = ±2), which is also assumed in the remainder of this thesis. In future work, however, it might be worthwhile to include rotational-vibrational Raman scattering in the radiative transfer models 3 . 3 Vibrational Raman scattering by N 2 and O 2 gives rise to “ghosts” of Fraunhofer lines at longer wavelengths. This
Page 1 and 2: VRIJE UNIVERSITEIT Rotational Raman
Page 5 and 6: Contents 1 Introduction 1 1.1 Obser
Page 7 and 8: 1 Introduction 1.1 Observing skylig
Page 9 and 10: Introduction 3 Extracting the wealt
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Page 17 and 18: Introduction 11 scattered radiance
Page 19 and 20: Introduction 13 approximation in wh
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56 Chapter 3 biases the simulation
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58 Chapter 3 3.4.2 Approximation me
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60 Chapter 3 where I ram,app and I
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62 Chapter 3 3.5 Simulation of pola
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64 Chapter 3 Figure 3.10: Relative
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66 Chapter 3 dependence on the vert
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68 Chapter 3 Figure 3.13: Same as F
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70 Chapter 3 3.6 Summary A vector r
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72 Chapter 3 where λ is the wavele
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74 Chapter 3 where S l is the expan
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76 Chapter 3 3.C Appendix: Evaluati
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4 Accurate modeling of spectral fin
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5 Retrieval of cloud properties fro
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Retrieval of cloud properties from
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References Aben, I., F. Helderman,
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References 121 Ellery, A., D. Wynn-
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References 123 Lacis, A. A., J. Cho
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References 125 Schulz, F., K. Stamn
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Summary A spectrum of sunlight that
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Summary 129 Earth radiance spectrum
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Samenvatting Het door de aardatmosf
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Samenvatting 133 met een vector-mod
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