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Matrix form of VRTE solution for verticaly stratified slabстатья
- Авторы: Brill A.I., Budak V.P., Ilyushin Ya A., Korkin S.V., Oshchepkov S.L.
- Сборник: PIERS 2009 in Moscow, August 18-21, 2009 [piers@ewt.mit.edu] http;//piers.mit.edu/piers2k9Moscow/programfinal.php http://piers.mit.edu/piers/ http://piers.mit.edu/piers2k9Moscow/files/Program.pdf http://piers.mit.edu/piers2k9Moscow/
- Год издания: 2009
- Первая страница: 347
- Аннотация: This paper presents a mathematical model of the spatial-angular distribution forthe reflected radiation polarization state. We have not assumed restrictions on the optical charac-teristics of scattering media such as those related to the artificial smoothness of the phase matrixelements. This model was developed for the purposes of validation study and precise processingof the satellite-borne data that would be available from the Greenhouse Gases Observing Satellite(GOSAT) [1] and from the Orbiting Carbon Observatory (OCO) [2]. We consider the scatteringmedium as a horizontally infinite and vertically inhomogeneous slab irradiated at an arbitraryangle by a plain unidirectional (PU) source of light. The bottom boundary (ground surface) isconsidered as a reflecting one with arbitrary BRDF.The physical basis for the radiative transfer theory is the ray approximation that causes spatialsingularities, described by Diracδ-function, in the solution of the vectorial radiative transferequation (VRTE). It is possible to formulate an equation upon the analysis of the spatial spectrumof the Stokes vector — the vectorial modification of the spherical harmonics method (VMSH). TheVMSH is an approximate solution of the VRTE that includes the solution singularities togetherwith the anisotropic part. The method proposed in this study provides a higher accuracy inradiative transfer modeling as compared with the small angle approximation [3]. The sourcefunction built upon the VMSH does not change the form of the VRTE boundary problem for theregular (smooth) part. The superposition of the VMSH (singular part) and a regular part givesthe complete solution of the VRTE boundary problem [3].The regular part of the boundary problem is solved using the Discrete Ordinates Method. Thesame method allows to obtain exact analytical solutions for the sampled VRTE in the matrixform and to describe the vertical heterogeneity of the slab through the division of the completeradiation flux upon the descending and ascending ones and thus to include the symmetry of theVRTE boundary problem for the case of PU source.The extraction of the singularities together with the anisotropic part upon the VMSH from thecomplete VRTE solution reduces time consuming in the modeling of reflected light polarizationand eliminates oscillation of the solution that would inherent to other methods. The resultsobtained form the basis for solving the problem of 3D polarized radiative transfer [3].REFERENCES1.Yokota, T., et al., “A nadir-looking ‘SWIR’ sensor to monitor CO2column density for Japanese‘GOSAT’ project,”Proceedings of the Twenty-fourth International Symposium on Space Tech-nology and Science, 887, Japan Society for Aeronautical and Space Sciences and ISTS,Miyazaki, 2004.2.Crisp, D., et al., “The Orbiting Carbon Observatory (OCO) mission,”Adv. Space Res., Vol. 34,700, 2004.3.Budak, V. P. and S. V. Korkin, “On the solution of vectorial radiative transfer equation inarbitrary three-dimensional turbid medium with anisotropic scattering,”JQSRT, Vol. 109,220, 2008
- Добавил в систему: Илюшин Ярослав Александрович