Solution of the transport equation in a three-dimensionally inhomogeneous scattering layer by the method of characteristics

Analysis of the Discrete Theory of Radiative Transfer in the Coupled “Ocean–Atmosphere” System: Current Status, Problems and Development Prospects

“…Hence, the solution can be expressed as the sum of the basic solutions according to the principle of superposition. Such a technique was considered in [10] and is referred to as the method of decomposition of BVPs. This method allows us to substitute the initial problem with boundary conditions with the hierarchy of BVPs that do not contain equations in boundary conditions.…”

“…Substituting the obtained result in Equations (10) and (12), after transformations and the inverse Fourier transform, one reaches a solution of the BVP (Equation (9)):…”

“…where C(ν) ≡ Rψ is the mean hemispherical albedo of the turbid medium slab. Accordingly, following [10] the solution of the BVP (Equation (1)) for an arbitrary layer with a reflecting Lambertian bottom can be reduced to a superposition of solutions:…”