A new scheme based on perturbation method is presented to solve the problem of solar/infrared radiative transfer (SRT/IRT) in a scattering medium, in which the inherent optical properties (IOPs) are vertically inhomogeneous. The Eddington approximation for SRT and the two-stream approximation for IRT are used as the zeroth-order solution, and multiple-scattering effect of inhomogeneous IOPs is included in the first-order solution. Observations show that the stratocumulus clouds are vertically inhomogeneous, and the accuracy of SRT/IRT for stratocumulus clouds by different solutions is evaluated. In the spectral band of 0.25–0.69 μm, the relative error in absorption with inhomogeneous SRT solution is 1.4% at most, but with the homogeneous SRT solution, it can be up to 7.4%. In the spectral band of 5–8 μm, the maximum relative error of downward emissivity can reach −11% for the homogeneous IRT solution but only −2% for the inhomogeneous IRT solution.
Part of the book: Perturbation Methods with Applications in Science and Engineering