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| Titel |
On the implementation of the discrete ordinate method with small-angle approximation for a pseudo-spherical atmosphere |
| VerfasserIn |
D. Efremenko, A. Doicu, D. Loyola, T. Trautmann |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250068426
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| Zusammenfassung |
| Numerical problems appear when solving the radiative transfer equation for systems with
strong anisotropic scattering. To avoid oscillations in the solution a large number of discrete
ordinates is required. As a consequence, the computing time increases considerably with
O(N3), where N is the number of discrete ordinates. The performance can be improved
partially by the delta-M method of Wiscombe [1], but this approach distorts the initial
boundary problem and can lead to errors in small viewing angles. The efficiency of the
discrete ordinate method with small-angle approximation for analyzing systems containing
clouds and coarsest fraction of aerosol has been demonstrated by Budak and Korkin
[2].
In this work we extend the plan-parallel version of the discrete ordinate method with
small-angle approximation, as described in [2], to a pseudo-spherical atmosphere. The
conventional pseudo-spherical technique relies on the separation of the total radiance into the
direct solar beam and the diffuse radiance [3];the direct solar radiance is treated in a spherical
geometry, while the diffuse radiance is computed in a plane-parallel geometry. Taking into
account that in the discrete ordinate method with small-angle approximation, the radiance is
separated into an ’anisotropic’ and a smooth part, and that the direct solar beam is already
included into anisotropic part, we introduce a pseudo-spherical correction by substracting the
direct solar beam in a plane-parallel geometry and adding it in a pseudo-spherical
geometry.
In our simulations we considered a scenario which is typically for the UV/UIS
instruments like GOME-2: a spectral interval between 315 nm and 335 nm, and an
inhomogeneous atmosphere containing a cloud layer with an asymmetry parameter of 0.9.
The numerical results evidenced that the differences between the pseudo-spherical and the
plan-parallel models are of about 10 % for an incident angle of 80 degrees, 1 % for 65
degrees and less than 0.3 % for 50 degrees. In addition to these simulations, we
compared two version of the discrete ordinate method, namely the discrete ordinate
methods with matrix exponential (DOME) [4] and the small-angle approximation. The
numerical analysis revealed that the small-angle approximation yields results of
acceptable accuracy (of about 1%) for a significantly lower number of discrete
ordinates.
References
1. Wiscombe W.J. The delta-M method. Rapid yet accurate radiative flux calculations for
strongly asymmetric phase functions // J. Atmos. Sci. 1977. V. 34, N 9. P. 1408-1422.
2. Budak V.P., Korkin S.V. On the solution of a vectorial radiative transfer equation in an
arbitrary three-dimensional turbid medium with anisotropic scattering // JQSRT. 2008. V.109.
P. 220-234.
3. Eddington A.S. On the radiative equilibrium of the stars // Mon. Notic. Roy. Astron.
Soc. 1916. V. 77. P. 16-35.
4. Doicu A., Trautmann T. Discrete-ordinate method with matrix exponential for
a pseudo-spherical atmosphere: Scalar case // JQSRT. 2009. V.110. P.146-158. |
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