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

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82 Chapter 4 corresponds to a Doppler shift of the calibrated solar spectrum of +0.009 nm at 395 nm. We found the shift between the solar spectrum wavelength grid and the earthshine wavelength grid increasing from 0.011 to 0.013 nm in the wavelength range 390–400 nm for a typical measurement. The difference between the observed shift and the theoretical Doppler shift might be explained by issues with the standard wavelength calibration of GOME [van Geffen and van Oss, 2003]. Instrumental effects such as detector temperature effects and the ellipticity of the Earth’s orbit might also play a role [Chance et al., 2005]. The earthshine radiance I pix that is measured by a certain detector pixel depends linearly on the solar spectrum F 0 and can be written as I pix = ∫ ∞ 0 k ear (λ)F 0 (λ) dλ , (4.1) where we assume that the solar spectrum F 0 is a continuous function of wavelength λ. The integral kernel k ear describes the transport of unpolarized solar radiation through both the Earth’s atmosphere and the GOME spectrometer. The atmospheric contribution can be summarized by the 4D reflectivity vector r. Its application to the solar spectrum provides the radiation illuminating the GOME entrance slit. This is described by the intensity vector I, which has the four Stokes parameters I, Q, U, and V as its components, and thus I(λ) = ∫ ∞ 0 r(λ,λ ′ )F 0 (λ ′ ) dλ ′ . (4.2) Here, the reflectivity r includes the effect of elastic scattering and inelastic Raman scattering in the Earth’s atmosphere that corresponds to a mapping of solar radiation from a wavelength λ ′ to a wavelength λ. In this paper we have used the vector radiative transfer model of Landgraf et al. [2004] in which a Gauss-Seidel iteration technique is used to solve the vector radiative transfer equation [Hasekamp and Landgraf , 2001]. This model has proven to be highly efficient for optically thin atmospheres [Hasekamp and Landgraf , 2001, van Diedenhoven et al., 2006]. The radiative transfer perturbation theory is employed by treating inelastic rotational Raman scattering as a perturbation to elastic Rayleigh scattering. One order of Raman scattering is included. Van Deelen et al. [2005] (Chapter 2) have shown that this approximation overestimates the filling in with at most 0.6% at the center of the Ca II lines, compared to a computationally expensive multiple Raman scattering calculation. For an appropriate description of the GOME earthshine measurements we also have to account both for the polarization sensitivity of the instrument and for the averaging of the measurements over the instrument’s field-of-view during a scan. For GOME, the radiance illuminating the detector device depends on the degree of polarization of the incoming radiation. The polarization sensitivity arises from the interaction of radiation with the different optical devices of the instrument. This dependence can be described by the scalar product I det = m · I , (4.3)
Accurate modeling of spectral fine-structure in Earth radiance spectra measured with GOME 83 where the vector m = (m 1 ,m 2 ,m 3 ,m 4 ) contains the corresponding elements of the instrument Mueller matrix [Coulson, 1988]. Presuming that the measurement to be simulated is the radiometrically calibrated, polarization sensitive measurement, the elements of vector m have to be normalized to its first component [Hasekamp et al., 2002], i.e. ( m = 1, m 2 , m 3 , m ) 4 . (4.4) m 1 m 1 m 1 The GOME instrument has a different sensitivity for radiation polarized parallelly and perpendicularly to the instrument’s optical plane. The sensitivity for radiation linearly polarized in a plane rotated by +45 ◦ and −45 ◦ with respect to the optical plane is assumed to be the same. Furthermore, we assume that GOME is not sensitive to circularly polarized radiation. This means that the elements m 3 and m 4 are zero. The ratio m 2 /m 1 was determined during the preflight calibration of GOME. Next, the averaging over the instrument’s field-of-view can be expressed by an integration over the scan angle ϑ between boundaries ϑ 1 and ϑ 2 , resulting in the expression Ī det = ∫ϑ 2 1 ϑ 1 −ϑ 2 ϑ 1 m · I dϑ . (4.5) Finally, we have to consider the spectral smoothing of the instrument including the spectral sampling by the detector array. This can be described by a twofold convolution of the intensity spectrum Ī det with an instrument slit function f and a sampling function g, viz. I pix = ∫ ∞ g(λ) ∫ ∞ f(λ,λ ′ )Īdet(λ ′ ) dλ ′ dλ . (4.6) 0 0 Here, the sampling and slit function may vary between the different detector pixels of the instrument. For many purposes it is convenient to combine the slit function f and the sampling function g to an instrument response function s, s(λ ′ ) = ∫ ∞ 0 g(λ)f(λ,λ ′ ) dλ , (4.7) which simplifies the notation of Eq. (4.6) to I pix = ∫ ∞ s(λ ′ )Īdet(λ ′ ) dλ ′ . (4.8) 0 The rationale for introducing the instrument response function is that it can be determined by using standard spectroscopic techniques, whereas the separate characterization of the slit and the sampling functions is extremely difficult. Therefore only the instrument response function was measured for
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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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A doubling-adding method to include
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Page 37 and 38: A doubling-adding method to include
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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 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: Accurate modeling of spectral fine-
Page 91 and 92: Accurate modeling of spectral fine-
Page 103 and 104: 5 Retrieval of cloud properties fro
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Page 125 and 126: References Aben, I., F. Helderman,
Page 127 and 128: References 121 Ellery, A., D. Wynn-
Page 129 and 130: References 123 Lacis, A. A., J. Cho
Page 131 and 132: References 125 Schulz, F., K. Stamn
Page 133 and 134: Summary A spectrum of sunlight that
Page 135 and 136: Summary 129 Earth radiance spectrum
Page 137 and 138: Samenvatting Het door de aardatmosf
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Samenvatting 133 met een vector-mod
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