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

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10 Chapter 1 1974]. In this thesis we choose to calculate them. The rotational Raman scattering cross section, which is a measure of the probability that light is scattered due to rotational Raman scattering, is given for each transition J →J ′ (e.g. [Chance and Spurr, 1997, Sioris and Evans, 1999]): σ ram (λ,λ in ) = 256π2 27 (λ)−4 [γ(λ in )] 2 f(T,J)b(J →J ′ ). (1.6) Here, f is the fractional population of the initial energy states, T is the air temperature, γ is the polarizability anisotropy of the molecule, and b are the Placzek-Teller coefficients for each energy transition J →J ′ (See Appendix 3.A and 2.A and references therein for more details). The quantities f, γ, and b are different for N 2 and O 2 . According to Sioris [2001] the modeled and measured line strengths agree well within the experimental error of the measurements made by Penney et al. [1974] with differences of ±0.4% for N 2 and ±2% for O 2 . To get the Raman cross sections for air the cross sections of the different molecules have to be weighted according to their abundance, i.e. weighted with 0.7809 and 0.2095 for N 2 and O 2 , respectively. Eq. 1.6 allows one to calculate the probability ω(λ,λ in ) that light is scattered from a wavelength λ in to a different wavelength λ. Figure 1.4 shows this probability distribution for λ in = 400 nm. The central line in the spectral scattering distribution shown in Fig. 1.4 is called the Cabannes line. Fig. 1.4 shows that only a small fraction of the light, approximately 4%, is scattered inelastically due to Raman scattering. The grey lines in Fig. 1.4 are associated with N 2 and the black lines with O 2 . Due to their spherical symmetry Ar atoms are not able to transfer rotational energy to the scattered light and hence show no Raman scattering. At each wavelength sunlight is scattered according to a spectral distribution that is similar to one that is shown in Fig. 1.4. Fig. 1.5 demonstrates how this leads to filling-in structures in a reflectivity spectrum. At the center of a Fraunhofer line the scattered light is less intense than at a continuum wavelength (Fig. 1.5 (a)). More light is scattered from the continuum into a Fraunhofer line than the other way around. This results in filling-in structures in a reflectivity spectrum (Figs. 1.5 (b) and (c)).
Introduction 11 scattered radiance solar irradiance a) wavelength (ir)radiance reflectivity b) c) Sun Earth wavelength Figure 1.5: Schematic illustration to explain the filling-in of Fraunhofer lines in an Earth radiance spectrum. We assume that the solar spectrum contains one artificial triangular Fraunhofer line. (a) For each wavelength and in each scattering event, approximately 4% of the solar radiation is scattered to other wavelengths. The scattered radiance is of much lower intensity at the center of a dark Fraunhofer line than at the continuum. (b) The upper curve shows the solar irradiance spectrum again. The lower curve shows the Earth radiance with rotational Raman scattering taken into account (solid curve) and when all scattering would be purely elastic (Rayleigh scattering approximation, dashed curve). (c) The reflectivity spectrum which involves the ratio of the Earth radiance and the solar irradiance spectrum is featureless when all scattering is elastic (dashed curve), but shows a filling-in feature when rotational Raman scattering is included (solid curve).
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
Page 11 and 12: Introduction 5 and Spurr, 1997, Vou
Page 13 and 14: Introduction 7 energy: E rot (v,J)
Page 15: Introduction 9 Figure 1.4: Probabil
Page 19 and 20: Introduction 13 approximation in wh
Page 21 and 22: Introduction 15 scattering have bee
Page 23 and 24: 2 A doubling-adding method to inclu
Page 25 and 26: A doubling-adding method to include
Page 43: A doubling-adding method to include
Page 46 and 47: 40 Chapter 3 nm with a spectral res
Page 48 and 49: 42 Chapter 3 contributions of lower
Page 50 and 51: 44 Chapter 3 if we use the effectiv
Page 52 and 53: 46 Chapter 3 This in turn results i
Page 54 and 55: 48 Chapter 3 This may be shown in a
Page 56 and 57: 50 Chapter 3 The forward and adjoin
Page 58 and 59: 52 Chapter 3 Here, ∆ = diag [1, 1
Page 60 and 61: 54 Chapter 3 Figure 3.3: Relative R
Page 62 and 63: 56 Chapter 3 biases the simulation
Page 64 and 65: 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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