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

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32 Chapter 2 scattering event. In both cases the nth order term of the Dyson series represents the contribution of n order of Raman scattering to the Green’s operator G. For numerical applications, we truncate the Dyson series in first order, hence G ≈ G o − G o ∆LG o . (2.23) Now the differences between the two applications of the perturbation theory become clear, i.e. resulting from the the different choice of both G 0 and ∆L. In the case of the unperturbed problem including purely Cabannes scattering, Raman scattering processes of second order and higher are ignored, whereas in the second case these scattering processes are effectively described by Rayleigh scattering. In that sense both applications correspond to approaches A and B mentioned above. The corresponding numerical applications of the perturbation theory will be referred to as the PTA and the PTB model. First of all, we compared PTA model simulations with DA1 simulations. Here it is important to notice that, although both models describe multiple Cabannes scattering and one order of Raman scattering, they do not solve exactly the same problem. The DA1 model takes into account that a Raman scattering event influences the succeeding propagation of light. This is not the case for the PTA model. The propagation before and after the perturbation is kept fixed, as can be seen in the second term in Eq. (2.23), where G o describes the propagation of scattered light in a pure Cabannes scattering atmosphere. However, the model simulations show that this is only a minor effect that causes differences less than 0.005% between the simulated radiance spectra. Figure 2.5: Absolute difference in filling-in between the perturbation theory model result (PTA and PTB) and the doubling-adding model result (DA). Lines are drawn for approach A (PTA, dotted line), where a Cabannes scattering atmosphere is taken as the base problem, and for approach B (PTB, solid line), where a Rayleigh scattering atmosphere is taken as the base problem. The same model parameters were used as in Fig. 2.4. Fig. 2.5 presents the comparison of both PTA and PTB model simulations with DA simulations, which include multiple Raman scattering. Shown is the absolute difference in the filling-in spectra
A doubling-adding method to include multiple orders of rotational Raman scattering 33 Figure 2.6: The reflectivity R(∆ν)≡R(ν, µ v , ϕ v ; ν ′ in , µ 0, ϕ 0 ) versus wavenumber shift ∆ν = ν−ν ′ in for incoming light at ν ′ in = 25316 cm−1 (λ = 395 nm). The upper panel shows the reflectivity calculated with DA, the middle shows the differences between PTA and DA, and the lower panel shows the differences between PTB and DA. The differences are given with respect to the reflectivity of a Rayleigh scattering atmosphere. The same model atmosphere parameters were used as in Fig. 2.4. Note that the difference in the elastic component between PTB and DA (lower panel) is -0.41%, and falls outside the vertical plot range.
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 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 37: 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
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
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Accurate modeling of spectral fine-
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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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