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

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52 Chapter 3 Here, ∆ = diag [1, 1, −1, −1] and Z m , Ψ ±m i and I +m are the Fourier components of the scattering phase matrix, the pseudo-forward and forward intensity field, respectively (see Eq. (3.81) and (3.86) in Appendix 3.B). Analogously, we obtain a corresponding sines expansion for the radiation effects E i , with i=3, 4, K i (λ,λ v ) = π ∞∑ (2−δ m0 ) sin[m(ϕ v −ϕ 0 )]Ki m (z,λ,λ v ) (3.53) 4 with coefficients K m i (λ,λ v ) = m=0 ∫ 1 ∫ 1 { dz β scat (z,λ,λ v ) dµ d˜µ −1 −1 } i (z,µ,λ v )∆Z m (λ, ˜µ,µ)I +m o (z, ˜µ,λ) . (3.54) ∫ ztop 0 Ψ −mT To determine the coefficients in Eqs. (3.51) and (3.54), any vector radiative transfer model may be used that calculates the Fourier components of the internal intensity fields I and Ψ i . A further evaluation of the perturbation integrals can be performed in a straightforward manner, but it relies on the specific solution technique used for the radiative transfer problem. Appendix 3.C gives an analysis of the integrals utilizing the Gauss-Seidel iteration method to solve the radiative transfer problem. This solution method is used for all numerical simulations presented in this paper. 3.4 Simulation of reflectance spectra 3.4.1 Rotational Raman scattering and polarization spectra To study the effect of Raman scattering on the intensity vector of backscattered light, we consider simulated spectra of I, Q and U of the reflected light in a nadir viewing direction at the top of cloudfree and aerosol-free model atmospheres. The simulations are performed on a 1 cm −1 spectral grid from 290-405 nm. Due to the specific form of the phase matrix for Raman, Rayleigh and Cabannes scattering (see Eq. (3.78) of Appendix 3.A), the Stokes parameter V always vanishes for these model atmospheres. The spectra are convolved with a Gaussian slit function with a FWHM of 18 cm −1 , which corresponds to a FWHM of 0.15–0.29 nm depending on wavelength. Figure 3.2 gives two examples of simulated spectra I/F 0 , Q/F 0 , and U/F 0 for solar zenith angles ϑ 0 = 10 ◦ and 70 ◦ . Ozone absorption is included in the model calculations, which causes a low reflectance at wavelengths below 320 nm. The decrease in reflectance toward longer wavelength is due to the λ −4 wavelength dependence of Rayleigh scattering. Overall the polarization components Q and U are one order of magnitude smaller for ϑ 0 = 10 ◦ than for ϑ 0 = 70 ◦ , which is primarily caused by the difference in the single scattering geometry. The corresponding Ring spectra in I, Q and U are depicted in Fig. 3.3. Here, a Ring spectrum is defined by R I = I ram − I ray I ray (3.55)
A vector radiative transfer model using the perturbation theory approach 53 for the radiance component and corresponding expressions hold for the other Stokes parameters. I ray represents the reflected intensity, simulated for a Rayleigh scattering atmosphere, and I ram denotes the same intensity but taking Raman scattering into account in the simulation. At the center of the strong Ca II K and H Fraunhofer lines at 393.5 and 396.8 nm rotational Raman scattering causes a filling-in of the Fraunhofer lines in I of 7% for ϑ 0 = 10 ◦ but of 12% for ϑ 0 = 70 ◦ . This dependence on solar zenith angle has been noted before [Joiner et al., 1995, Vountas et al., 1998] and can be explained by a difference in the scattering geometry. Ring structures in R Q are relatively small for ϑ 0 = 70 ◦ (less than 1%) but are more pronounced for the solar zenith angle ϑ 0 = 10 ◦ (up to 3.5%). Structures in R U are weak for both solar geometries. Figure 3.2: reflectance spectra I/F 0 , Q/F 0 , and U/F 0 at the top of a Rayleigh scattering atmosphere. Simulations are performed for solar zenith angles ϑ 0 = 10 ◦ (left panel) and ϑ 0 = 70 ◦ (right panel), for a viewing zenith angle ϑ v = 10 ◦ and for a relative azimuthal angle of 120 ◦ . The vertical distribution of ozone is adopted from the US standard atmosphere [NOAA, 1976], where the model atmosphere is divided in 60 homogeneous layers of the geometric thickness of 1 km. The Lambertian surface albedo is 5%. The solar spectrum F 0 is given by Chance and Spurr [1997], which has a spectral resolution of 1 cm −1 and is sampled at 1 cm −1 intervals.
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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 and 16: Introduction 9 Figure 1.4: Probabil
Page 17 and 18: Introduction 11 scattered radiance
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 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
Page 66 and 67: 60 Chapter 3 where I ram,app and I
Page 68 and 69: 62 Chapter 3 3.5 Simulation of pola
Page 70 and 71: 64 Chapter 3 Figure 3.10: Relative
Page 72 and 73: 66 Chapter 3 dependence on the vert
Page 74 and 75: 68 Chapter 3 Figure 3.13: Same as F
Page 76 and 77: 70 Chapter 3 3.6 Summary A vector r
Page 78 and 79: 72 Chapter 3 where λ is the wavele
Page 80 and 81: 74 Chapter 3 where S l is the expan
Page 82 and 83: 76 Chapter 3 3.C Appendix: Evaluati
Page 85 and 86: 4 Accurate modeling of spectral fin
Page 87 and 88: Accurate modeling of spectral fine-
Page 103 and 104: 5 Retrieval of cloud properties fro
Page 105 and 106: Retrieval of cloud properties from
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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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