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

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8 Chapter 1 a) hc ν virtual energy level hc ν b) c) hc ν hc( ν− ∆ν) hc ν hc( ν+ ∆ν) Cabannes ∆J=0 i=f Stokes f i i ∆J=+2 ∆J =−2 f Anti−Stokes Figure 1.3: Molecular scattering involves an incident photon that brings a molecule with initial energy state i to a virtual energy state (dashed line). Subsequently, the molecule falls back to a lower energy state f by releasing a photon. If this final state f has the same energy as the initial state i the scattering process is said to be elastic and corresponds to Cabannes scattering (a). When the released photon has a lower energy than the incident photon (E f > E i ) the process is called Stokes rotational Raman scattering (b). When the released photon gains energy (E f < E i ) the scattering process is called anti-Stokes rotational Raman scattering (c). The net rotational energy transitions have to obey the quantum law ∆J = ±0, 2. We restrict ourselves to pure rotational Raman scattering processes (∆v=0; ∆J = ±2). Rotational Raman scattering by air molecules that involves a released photon with less energy than the incident one (∆J = +2; Fig. 1.3b) is referred to as Stokes rotational Raman scattering and inelastic scattering that involves an energy gain of the released photons (∆J = −2 ; Fig. 1.3c) is called anti- Stokes rotational Raman scattering [Young, 1982]. The energies of the anti-Stokes rotational Raman photons are given by hcν = hcν in + (4hcB 0 − 6hcD 0 )(J − 1 2 ) − 8hcD 0(J − 1 2 )3 , J = 2, 3,... , (1.4) and the energy of the Stokes rotational Raman photons are given by hcν = hcν in − (4hcB 0 − 6hcD 0 )(J + 3 2 ) + 8hcD 0(J + 3 2 )3 , J = 0, 1,... , (1.5) where hcν in is the energy of the incident light (see e.g. Fish and Jones [1995].) The energy shifts, and thus the wavenumber shifts ν−ν in , only adopt discrete values. It is important to realize that these fixed shifts in energy lead to wavelength shifts λ−λ in that are not fixed with respect to the wavelength of the incident light λ in . At shorter wavelengths the shifts in terms of wavelength are smaller than at longer wavelengths. This makes the use of wavenumbers more elegant and simple to describe the Raman effect. Nevertheless, both descriptions are used throughout this thesis. The line-strengths of the individual rotational Raman lines can be measured in the laboratory or can be calculated from theory (e.g. [Chance and Spurr, 1997, Burrows et al., 1996, Penney et al., scattering process involves much larger energy shifts than pure rotational Raman scattering, i.e. -2331 cm −1 and -1555 cm −1 for N 2 and O 2 , respectively. For incident light at 400 nm, this corresponds to wavelength shifts of +41.1 nm and +26.5 nm for N 2 and O 2 , respectively. Burrows et al. [1996] estimated that the largest spectral features caused by vibrational Raman scattering are expected to be maximally 0.27% in GOME reflectivity spectra.
Introduction 9 Figure 1.4: Probability ω that incoming radiation with λ in =400 nm is scattered to a certain wavelength λ. Together, the rotational Raman lines make up approximately 4% of the total scattered radiation. The parcel of air was assumed to be composed of N 2 , O 2 and Ar only and to have standard temperature and pressure (T = 273.15 K and p = 1023.25 hPa). The rotational Raman lines of N 2 and O 2 are shown in grey and black, respectively. Absorption and scattering by other atmospheric constituents such as water, aerosols, nitrogen dioxide, ozone and carbon dioxide are ignored. The wavelength range 400±4 nm corresponds to the wavenumber range 25000∓250 cm −1 .
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: Introduction 7 energy: E rot (v,J)
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 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
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58 Chapter 3 3.4.2 Approximation me
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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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