Abstract
New nonlinear integral equations of the radiative transfer theory for determination of unified function combining the intensities of upgoing and downgoing radiation at arbitrary symmetrical levels of a uniform slab has been obtained using the Ambarzumian-Chandrasekhar classical invariance principle. By applying the mirror reflection principle proposed by the author, the unified function and photometrical invariants concept is considered. Based on fitting parametrization of the obtained nonlinear integral equation in the case of strongly elongated phase functions, the spatial-angular structure of inner radiation fields is represented as primary scattering radiation and adaptive fitting factors conditioned by multiple radiation scattering in a uniform slab. Numerical modelling has been carried out for the obtained approximate solutions of the nonlinear integral equations for the Henyey-Greenstein phase function with parameter \( g \ge 0.9 \) and representative models of optical parameters of Earth’s aerosol atmosphere. The accuracy of obtained approximate relations has been evaluated also. The obtained fitting analytical expressions have clear physical meaning and can be used for the statement and numerical modelling of direct and inverse problems solutions in the radiative transfer theory and natural environments optics.
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Smokty, O.I. (2016). Analytical Spatial-Angular Structure of Uniform Slab Radiation Fields for Strongly Elongated Phase Functions. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_9
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DOI: https://doi.org/10.1007/978-3-319-42085-1_9
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