![]() ![]() It allows the algorithm to use radiance data with multiple views of the same pixel as an input and produce correct output even for large solar zenith or satellite view angles, when an independent pixel approximation fails. The combination of the GC approach and the effective inverse algorithm creates an extremely useful and efficient tool for extraction of cloud fields from satellite imagery. The algorithm can be applied to the plane-parallel radiative transfer as well as to the GC method. ![]() Typically, two to three iterations are enough in order to obtain a solution with sufficiently high accuracy. The algorithm convergence rate is very high. This algorithm modifies the DOM using Newton’s iterative scheme in order to find a solution of the inverse problem. The modification has another important advantage in that it permits obtaining particular solutions for both infrared and direct beam radiative transfer in one computational step.Īn effective algorithm for solving inverse radiative transfer problems has been developed following the above reformulation. The same requirement on the scales of variations applies to the current method: length of horizontal variations of optical properties of the medium should be large in comparison to the mean radiative transport length. This treatment of the source term is similar to the gradient correction (GC) method, presented in the first part of the paper for the diffusion approximation. The modification is based on an expansion of the direct beam source term. The forward discrete ordinate method (DOM) has been reformulated to include effects of a weak inhomogeneity of a medium. The original optical depth shown by dotted line. (b) Optical depths retrieved from the above reflectances using IPA method (dashed and dash–dot lines) and simultaneously from both sets using two point-of-view algorithm (solid line). Relative azimuthal angle ϕ 0 − ϕ is 0 in both cases. The cloud was illuminated by a beam with μ 0 = 0.4. (a) Spatial distribution of reflectances at μ 2 = 0.707 view (dashed line) and at nadir μ 1 = 1.0 view (dash–dot line) used as input for the retrieval. (b) The same as in (a), but for backward reflectance ( μ 1 = 0.7, ϕ 0 − ϕ 1 = π).Īn example of retrieval of optical depth of Gaussian-shaped cloud using two point-of-view data. (a) Plot of forward reflectances for the gradient correction method (dashed), the IPA (dotted), and for 3D spherical harmonics discrete ordinate method (solid), where μ 1 = 0.7, ϕ 0 − ϕ 1 = 0 and all other parameters the same as in Fig. (d) The same as (b), but using different illumination angle μ 0 = 0.3 and ϕ 0 = π. (c) Plot of nadir reflectances for the gradient correction approximation with 0 (IPA) and 1 term in expansion (dotted and dashed curve respectively) and for 3D spherical harmonics discrete ordinate method (solid curve) calculated for the above 2D cloud field with μ 0 = 0.3 and ϕ 0 = 0. (b) Plot of the optical depth τ and the gradient correction parameter h 1( x) (dashed line) for the above 2D cloud field. 1996) used as a more “realistic” input cloud field. (a) Contour lines of 2D large-eddy simulation of clouds ( Moeng et al. Optical depth profile shown by bottom curve. (a) Plot of nadir reflectances for the gradient correction approximation with 0 (IPA), 1, and 2 terms in expansion (dotted, dashed, and dash–dot curve, respectively) and for 3D spherical harmonics discrete ordinate method (upper solid curve), where τ = 2, τ( x) = kH 0( x) = k Z, k = 7 km −1, δ = 0.75, Z = 0.5 km, g = 0.85, L x = 14.08 km, μ 0 = 0.3. ![]()
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