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

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12 Chapter 1 1.4 Accurate simulation of reflectivity spectra Traditionally, radiative transfer theory deals with elastic (Rayleigh) scattering in plane-parallel atmospheres (e.g. Mishchenko et al. [2006]). The Earth’s atmosphere is modeled as a stack of homogeneous model atmosphere layers that have an infinite horizontal extent. Obviously, with this approximation we cannot describe the observed filling-in structures in reflectivity measurements by GOME and similar instruments. An appropriate description of inelastic Raman scattering in atmospheric radiative transfer modeling, which is the subject of this thesis, is one of the two major challenges in atmospheric radiative transfer modeling. The other is the inclusion of three-dimensional effects such as broken cloud fields (e.g. Marshak and Davis [2005]) and the sphericity of the Earth (e.g. Walter et al. [2006], Spada et al. [2006], Postylyakov [2004]). 1.4.1 Polarization aspects of light Light can be described by a superposition of many continuous electric and magnetic fields that oscillate in space and time. Expression for these electromagnetic fields can be derived from classical electrodynamics which is founded on the Maxwell equations (e.g. Jackson [1975], Bohren and Huffman [1983], Mishchenko et al. [2004]). In practice these fast-oscillating electric and magnetic fields are not measured by satellite instruments, but a time-averaged energy flux is obtained. In 1852, G. G. Stokes suggested to describe a beam of radiation with the intensity vector ⎡ I(λ) = ⎢ ⎣ I(λ) Q(λ) U(λ) V (λ) ⎤ ⎥ ⎦ , (1.7) which has the four Stokes parameters I, Q, U, and V as its components. Here, I is the specific intensity and the parameters Q, U and V describe the state of polarization. They can be determined through intensity measurements only with the help of a polarizer and a phase retarder (e.g. Mishchenko et al. [2006], Coulson [1988]). The quantities I, Q, U and V are defined with respect to a certain reference plane, which is the local meridian plane in this thesis. For the interpretation of GOME, SCIAMACHY, OMI, and GOME-2 measurements a vector radiative transfer model is needed which includes inelastic Raman scattering, because of three reasons: The Stokes parameters are coupled due to scattering – Incident sunlight is unpolarized (Q = U = V = 0), but via (multiple) scattering in the Earth’s atmosphere and via reflection by the surface Q and U attain values due to the coupling that takes place between the different Stokes parameters in each scattering event. For most purposes, the Stokes parameter V that is associated with circular polarization can be ignored concerning light scattering by the Earth’s atmosphere and reflection by the Earth’s surface. This is not true for the Stokes parameters Q and U. From standard elastic (Rayleigh) scattering theory it is known that neglecting the coupling between the Stokes parameters I, Q, U leads to significant errors in the intensity that can be as large as 10% [Chandrasekhar, 1960]. This
Introduction 13 approximation in which the polarization aspects of radiation are ignored is referred to as the scalar approximation. Most instruments are polarization sensitive – The GOME, SCIAMACHY and GOME-2 instruments are sensitive to the polarization of the incident radiation, mainly due to the gratings in these instruments. Thus, for a proper measurement simulation it is therefore important to know the polarization sensitivity of the spectrometer as well as the intensity vector, including its polarization properties, that illuminates the entrance slit of the instrument [Hasekamp et al., 2002]. Ring structures appear in the polarization signal – Figure 1.6 shows a spectrum of the degree of linear polarization of zenith skylight, which is defined as P = √ Q 2 + U 2 /I. This spectrum was measured with a copy of the GOME spectrometer on the rooftop of SRON - Netherlands Institute for Space Research in Utrecht. A polarization filter was used in front of the spectrometer to measure the polarization spectra [Aben et al., 1999, 2001]. The figure shows that the Ring effect not only affects the reflectivity spectrum, but influences the polarization spectrum as well. This phenomenon that the degree of linear polarization is lower at the Fraunhofer lines than in the continuum was first reported by Noxon and Goody [1965]. Clearly, a vector radiative transfer model is needed that takes the different polarization characteristics of rotational Raman scattering and elastic Cabannes scattering into account. This means that the radiative transfer is further complicated: One has to take into account not only scattering from one direction to another, but also from one wavelength to another, while keeping track of the polarization state. Figure 1.6: The degree of linear polarization P = √ Q 2 + U 2 /I of zenith skylight as function of wavelength λ. This spectrum was determined on June 3, 1997 with a ground-based copy of the GOME spectrometer making use of a polarization filter. The solar zenith angle was 68 degrees. This figure has been adapted from Stam et al. [2002].
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: Introduction 11 scattered radiance
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
Page 66 and 67: 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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