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

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64 Chapter 3 Figure 3.10: Relative error δI conv in the polarization corrected radiances I conv due to the neglect of Ring structures in the relative Stokes parameter q in Eq. (3.61). Calculations are performed for the same model atmosphere as in Fig. 3.2 with ϑ 0 = 70 ◦ , ϑ v = 10 ◦ , and for relative azimuthal angle ∆ϕ = 120 ◦ . Figure 3.11: (left panel) Frequency distribution of the mean error of GOME reflectance measurements for the period April, 1996 - March 1998. Measurements are considered at 12 geo-locations, viz. ±60 ◦ and ±20 ◦ latitude and 0 ◦ , 120 ◦ and 240 ◦ longitude. Here, the distribution is binned in intervals of width 0.01 %. (right panel) Two GOME error spectra representing an upper and a lower error margin for GOME measurements. The solid line shows a 1 σ error spectrum with a mean error of ε=0.43%, the dotted line represents a corresponding spectrum with ε=0.19%.
A vector radiative transfer model using the perturbation theory approach 65 can be interpreted as a measure of the conversion bias. Obviously, b mean depends on the selected spectral range of the measurement. In the following we consider two examples: (a) the spectral range 290–313 nm, which can be used for ozone profile retrieval (see e.g. Hasekamp and Landgraf [2001]) and (b) two detector bins related to the center of the Ca II K and H Fraunhofer lines at 393.5 and 396.8 nm, which contain information on the cloud distribution of the observed ground scene [Joiner and Bhartia, 1995]. In the case of ozone profile retrieval the mean relative bias b mean due to the neglect of Raman scattering in the polarization correction is 0.3 and 0.7 for the error scenarios e max and e min , respectively. This indicates that the mean bias is below the instrument noise for this application. However, at the center of the Ca II Fraunhofer lines b mean reaches values of 10.0 and 11.34 for both error scenarios. So in this case the bias is 10 times as large as the instrument noise, which can cause serious problems for the interpretation of the filling-in of these Fraunhofer lines. For retrieval purposes the polarization correction can be avoided, if one attempts to reproduce the polarization sensitive measurement I pol,i instead of a polarization corrected radiance measurement. For GOME this requires the simulation of Stokes parameters I i and Q i of the backscattered sunlight. Hasekamp et al. [2002] have demonstrated that this approach provides a clear improvement for ozone profile retrieval from GOME reflectance measurements, compared to a retrieval approach using polarization corrected radiances. The retrieval approach utilizes measurement simulations, which are performed for a Rayleigh scattering atmosphere. To include Ring structures in the simulations one may introduce Ring spectra in the different Stokes parameters of the polarization sensitive GOME measurement in Eq. (3.60), viz. I pol = (1 + R I,vec )I ray,vec + m 12 (1 + R Q,vec )Q ray,vec . (3.65) To simplify matters we omit the pixel index i on the spectra. For an efficient simulation of polarization sensitive GOME measurements one can try to approximate the Ring structures of I pol by a simplified calculation scheme. The results of the previous section suggest to neglect the Ring spectrum R Q,vec in Eq. (3.65) because of its small value. Thus we first consider the approximation I app1 = (1 + R I,vec )I ray,vec + m 12 Q ray,vec . (3.66) Subsequently, we replace the Ring spectrum R I,vec by the respective scalar and single scattering spectra, which yields the approximations I app2 = (1 + R I,sca )I ray,vec + m 12 Q ray,vec , (3.67) I app3 = (1 + R I,ssc )I ray,vec + m 12 Q ray,vec . (3.68) In the context of GOME measurement simulations the goodness of these approximations can be assessed using the mean relative bias b mean in Eq. (3.64) with b i = I app,i − I pol,i . Again we consider the mean bias for the spectral range 290-313 nm as well as at the center of the Ca II Fraunhofer lines. Figure 3.12 shows b mean for the spectral window of ozone profile retrieval as functions of the solar zenith angle, of the viewing zenith angle and of the relative azimuthal angle for a fixed model atmosphere. The dependence on atmospheric parameters is demonstrated in Fig. 3.13, which shows the
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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
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
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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 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 103 and 104: 5 Retrieval of cloud properties fro
Page 105 and 106: Retrieval of cloud properties from
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Retrieval of cloud properties from
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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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