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

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92 Chapter 4 for a possible erroneous wavelength calibration of GOME. Temperature and pressure profiles were adopted from the UK MetOffice database for the observed scene. The mean residual for the earthshine measurements over land is shown in Fig. 4.6, as a function of detector pixel. The Earth radiance noise is low in the range 390–400 nm and ranges from 0.05% to 0.2% at the center of the Ca II Fraunhofer lines. The rms of the noise is approximately 0.08%. We see that the high frequency features in the mean residual are similar to the undersampling error in Fig. 4.5. Here, the differences could be explained by (1) differences between the reference highresolution solar spectrum used in Fig. 4.5 and the real high-resolution solar spectrum, (2) calibration errors that affect the Earth and solar measurements in a different way, and (3) possible errors in the Earth radiance forward model, which could be instrumental (e.g. incorrect instrument response function) or atmospheric (e.g. incorrect treatment of Raman scattering). The fact that the mean Figure 4.6: Mean residual for the earthshine measurements over land in the two selected GOME orbits ((a) 25 earthshine spectra in 80702165, (b) 121 earthshine spectra in 81003031), using the reconstructed solar spectrum on a 1 cm −1 grid from the GOME solar measurement. The light gray area corresponds to the mean residual ± 1 standard deviation. The earthshine wavelengths of earthshine measurement 967 in orbit 80702165 were assigned to the detector pixels. residuals for both orbits are similar and that their spread is of the same order as the measurement noise confirms that the undersampling error is very stable along the orbit, at different dates, and at different locations [Slijkhuis et al., 1999, Chance et al., 2005]. This is directly related to the shift between the solar irradiance spectrum and the Earth radiance spectrum, which does not change significantly within one orbit. Moreover, the wavelengths assigned to each detector pixel show no significant variation for the Earth radiance measurements.
Accurate modeling of spectral fine-structure in Earth radiance spectra measured with GOME 93 4.5 Retrieval of a solar spectrum on a fine spectral grid from the combination of an earthshine and a solar measurement To reduce the undersampling error discussed in Section 4.4, we present a retrieval scheme to determine a solar spectrum from the combination of a solar irradiance and an Earth radiance measurement. This combination allows a significant reduction of the undersampling error for two reasons: First, the shift between the solar wavelength grid and the Earth wavelength grid makes the solar irradiance measurement and the Earth radiance measurement two differently sampled representations of the same underlying high-resolution solar spectrum. Second, the Earth and solar wavelength grids are very stable (Section 4.4.3). The inversion scheme described in Section 4.4.1 can be adopted in a straightforward way to retrieve a solar spectrum x on a fine spectral grid from the combination of Eqs. (4.11) and (4.12), i.e. ( ) y ear = y sun ( ) K ear x + K sun ( ) e ear . (4.18) e sun Here the number of measurements is increased from M to 2M, which results in the 2M dimensional measurement vector y = (y ear ,y sun ) T with the corresponding error vector e y = (e ear ,e sun ) T . Furthermore, the kernel matrix K = (K ear ,K sun ) T is a 2M × N matrix. Apart from the effect of the atmosphere on the Earth radiance spectrum, the additional measurement components result in an effectively increased sampling of the incident solar spectrum, and in turn reduces the undersampling problem. To obtain the solar spectrum from the combination of both measurements, we again employ the minimum length solution in Eq. (4.15). Owing to the use of both measurements, the rms of the null-space component decreases significantly from 23.4% to 20.1%, and thus the row space component contains more spectral fine-structure. This improvement arises mainly from the two different samplings of the solar and earthshine spectra. Here atmospheric effects such as the extra smoothing attributable to Raman scattering (see Fig. 4.1) are less important. When applying this approach, it is important that the unknown atmospheric and surface parameters that affect the earthshine spectrum can be retrieved simultaneously with the solar spectrum. Other geophysical parameters have to be assumed a priori. To fulfill this condition as well as possible, we select an Earth radiance spectrum of a clear sky scene over land (by making use of the cloud filter in Krijger et al. [2005]), i.e. a measurement that is not affected by clouds or underwater scattering in the ocean. For such a scene we consider the surface albedo and its linear dependence on wavelength as the only unknown geophysical parameters. Additionally, we include a wavelength shift ∆λ in the instrument response function in Eq. (4.9) as an additional fit parameter to correct for a possible wavelength calibration error. To demonstrate that the undersampling problem of GOME can be significantly reduced by this approach, we combined the Earth radiance spectrum number 967 in GOME orbit 80702165 and the Earth radiance spectrum number 800 in GOME orbit 81003031 with the corresponding solar spectra. Then, in the same way as described in Section 4.4.3, the retrieved solar spectra were used to model the remaining Earth radiance spectra of all clear sky measurements over land of both orbits.
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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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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 and 88: Accurate modeling of spectral fine-
Page 97: 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,
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
Page 139 and 140: Samenvatting 133 met een vector-mod
Page 141: List of publications Peer-reviewed
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