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

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70 Chapter 3 3.6 Summary A vector radiative transfer model is presented that includes the simulation of inelastic rotational Raman scattering in addition to elastic Cabannes scattering. The model describes the reflectance properties of a vertically inhomogeneous, plane-parallel model atmosphere bounded below by a Lambertian surface. Rotational Raman scattering is treated as a perturbation to Rayleigh scattering. This perturbation is presented by a classical perturbation series using the Green’s function formalism of the unperturbed problem. The n-th contribution of the perturbation series describes the effect of n orders of Raman scattering. The model is worked out in more detail for first order perturbations. In this case the forward and the adjoint solutions of the radiative transfer problem replace the expensive calculation of the corresponding Green’s function, which provides a significant reduction in the numerical requirements. Based on this a numerical vector radiative transfer model is presented including one order of Raman scattering. For the calculation of the perturbation effect any vector radiative transfer model can be used that calculates the internal forward and adjoint intensity vector field of the atmosphere. In this paper the Gauss-Seidel iteration method is employed, which provides efficient simulations for cloud-free atmospheres. Simulations of Ring spectra are presented for the spectral range 290-405 nm and the effect of Raman scattering on the the polarization components Q and U is discussed. Here, Ring structures in the Stokes parameters Q and U originate both from the polarization of light by Raman scattering itself and from the polarization by Cabannes scattering following a Raman scattering process. In general, polarization Ring spectra of Q and U are much weaker than those of the radiance component due to the low polarization of Raman scattered light. Only for a low polarization of the reflected sunlight pronounced Ring structures occur in the polarization spectra. Those are mainly caused by the propagation of Ring structures from the radiance component to the polarization components by Cabannes scattering processes. However, because of the small degree of polarization of the reflected light, this effect is of minor importance for most applications. The accuracy of two common approximation techniques is investigated for an efficient simulation of Ring spectra: the single scattering approximation and the scalar approximation. The single scattering approach shows a clear bias in the simulation of Ring structures. For example, the filling-in of the Ca II Fraunhofer lines near 395 nm is underestimated by more than a factor of 2. The corresponding filling-in simulated with the scalar approach is only biased with a factor of about 1.01. The relevance of biases depends on the spectral range of the measurement and on the specific application. For example, for ozone profile retrieval from GOME polarization sensitive radiance measurements between 290–313 nm the combination of both a vector radiative transfer model, which simulates the measurement for a Rayleigh scattering atmosphere, with a scalar radiative transfer approach to account for the effect of inelastic Raman scattering on the measurement provides an efficient simulation of the measurement with only a minor bias. However, for the retrieval of cloud properties using the filling-in of the Ca II Fraunhofer lines of GOME radiance measurements we recommend comprehensive vector radiative transfer simulations of the Ring spectra in both Stokes parameters I and Q.
A vector radiative transfer model using the perturbation theory approach 71 3.A Appendix: Optical properties of rotational Raman, Cabannes and Rayleigh scattering In general, scattering of light by an ensemble of random oriented molecules is characterized by a scattering coefficient β scat and a scattering phase matrix Z. Here, the scattering coefficient may be written as β scat = σ ρ, (3.69) where σ is the scattering cross section and ρ the volume density of scattering molecules. The Rayleigh scattering cross section for a constituent of the atmosphere is given by [Bates, 1984, Bucholtz, 1995, Naus and Ubachs, 2000] [ ] σ ray (λ) = 24π2 c 4 n 2 2 (λ)−1 F N0λ 2 4 n 2 k (λ) (3.70) (λ)+2 where λ is wavelength, n is the refraction index, N 0 is the molecular number density and F k is the King factor. Here, the refraction index n and the number density N 0 have to be taken for the same conditions, i.e., same temperature and same pressure. The King factor and the refraction index for N 2 and O 2 molecules are given by Bates [1984]. For inert gases like Ar the King factor is 1. The refraction index of Ar is adopted from Peck and Fisher [1964]. Cabannes scattering cross sections may be calculated from the corresponding Rayleigh cross sections in a straightforward manner, viz. σ cab (λ) = 18+ε(λ) 18+4ε(λ) σ ray(λ). (3.71) The factor f = (18+ε)/(18+4ε) describes the fraction of scattered light that is contained in the Cabannes line [Kattawar et al., 1981]. Here ε=(γ/α) 2 , γ is the anisotropy of the polarizability, and α is the average polarizability, which can be determined from the relation [ ] 9 n 2 2 (λ)−1 α(λ) = . (3.72) 16π 2 N0 2 n 2 (λ)+2 For N 2 and O 2 a parameterization of γ is given by Chance and Spurr [1997]. However, ε may be calculated as well directly from the King factor using the relation F k =1 + 2ε/9. Rotational Raman scattering consists of Stokes and anti-Stokes scattering. Stokes lines are characterized by the change in rotational angular momentum of a molecule J → J ′ = J + 2 for J = 0, 1, 2,..., anti-Stokes lines are indicated by the transition J → J ′ = J − 2 for J = 2, 3, 4,.... The scattering cross sections for pure rotational Raman scattering are [Long, 1977, Chance and Spurr, 1997] σ ram (λ,λ ′ ) = 256π2 27(λ ′ ) 4 [γ(λ)]2 f(T,J)b(J →J ′ ), (3.73)
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VRIJE UNIVERSITEIT Rotational Raman
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Contents 1 Introduction 1 1.1 Obser
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1 Introduction 1.1 Observing skylig
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Introduction 3 Extracting the wealt
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Introduction 5 and Spurr, 1997, Vou
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Introduction 7 energy: E rot (v,J)
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Introduction 9 Figure 1.4: Probabil
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Introduction 11 scattered radiance
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Introduction 13 approximation in wh
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Introduction 15 scattering have bee
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2 A doubling-adding method to inclu
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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
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 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
Page 125 and 126: 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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