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

More documents

Recommendations

Info

60 Chapter 3 where I ram,app and I ray,app are approximate radiance spectra and I ray,vec is the corresponding radiance spectrum simulated with the vector model. Figure 3.8 shows the errors in the single scattering Ring spectra R I,ssc , R Q,ssc , and R U,ssc . As expected, below 300 nm Ring structures are reproduced well by this approximation due to the small fraction of multiple scattering events at these wavelengths. With the increase of multiple scattering toward longer wavelengths also the error in the single scattering Ring spectra increases. For the radiance component the absolute error in the Ring spectra is generally less than 4% but can reach 7% at the Ca II lines for ϑ 0 =70 ◦ . Keeping in mind that the filling-in of this Fraunhofer lines is about 12%, this represents a clear bias of more than a factor of 2 in the simulation of Ring spectra. For the polarization components relatively large errors occur in R Q,ssc for a solar zenith angle ϑ 0 =10 ◦ . This fact confirms the interpretation that for this particular case Ring structures are mainly produced by elastic scattering processes following a Raman scattering event. Obviously, this effect cannot be simulated in the single scattering approximation. For the other polarization Ring spectra, where this propagation effect is of minor importance, the differences are much smaller and generally below 0.2%. Another widely used approximation method, if only radiances need to be simulated, is the scalar radiative transfer approach. The advantage of this approach is that it takes into account multiple scattering of light but at the same time greatly simplifies the calculations, which reduces the computational cost. However, neglecting polarization can cause errors in the modeled radiance of up to 10% [Chandrasekhar, 1960, Mishchenko et al., 1994, Lacis et al., 1998, Hasekamp et al., 2002]. The upper panel of Fig. 3.9 shows the error in the radiance component I. In the single scattering domain below approximately 300 nm the error is very small. For singly scattered light the scalar approximation yields the same radiance as the vector approach, because the incoming sunlight can be assumed unpolarized [Hansen and Travis, 1974a]. However, if a second scattering process takes place, which is very likely for wavelengths longer than 300 nm (see Fig. 3.7), the incoming light for this process is strongly polarized (see e.g. Mishchenko et al. [1994]). The radiance of this second order scattered light does not depend only on the radiance component of the incoming light but also on its Stokes parameters Q and U. Hence, a neglect of polarization leads to an incorrect value of the modeled radiance. The same is true for higher order scattering but here the effect is smaller. In Fig. 3.9 magnitude and sign of the error in the scalar radiative transfer depend additionally on the scattering geometry and on the orientation of successive scattering processes [Mishchenko et al., 1994]. For the simulation of Ring spectra R I,sca the scalar approach is much more exact than for simulations of the continuum. The errors, shown in Fig. 3.9 are mostly below 0.1% and reach their maximum of 0.14% for the Ca II lines for ϑ 0 = 70 ◦ . Again, compared with the filling-in of the Fraunhofer line of 12% this represents a bias of only a factor of about 1.01. The high accuracy can be explained by the fact that Raman scattered light is less polarized and so the coupling of the Stokes parameters due to scattering processes is of minor importance for the simulation of Ring spectra in I.
A vector radiative transfer model using the perturbation theory approach 61 Figure 3.9: (upper panel) Relative error δI ray in simulated radiance spectra I ray due to the scalar approximation of radiative transfer, δI ray = (I ray,sca − I ray,vec )/I ray,vec . (lower panel) Difference D I,sca in the radiance Ring spectra R I,sca and R I,vec for scalar and vector radiative transfer simulations, respectively, D I,sca = R I,sca − R I,vec . Here, both Ring spectra are normalized to the radiance spectrum of a Rayleigh scattering atmosphere simulated with the vector radiative transfer model. The model atmosphere, surface albedo, and solar and viewing geometry is the same as in Fig. 3.2.
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 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
Page 62 and 63: 56 Chapter 3 biases the simulation
Page 64 and 65: 58 Chapter 3 3.4.2 Approximation me
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 103 and 104: 5 Retrieval of cloud properties fro
Page 105 and 106: Retrieval of cloud properties from
Page 117 and 118:
Retrieval of cloud properties from
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?