A new radiative transfer method for solar radiation in a vertically internally inhomogeneous medium

The problem of solar spectral radiation is considered in a layer-based model, with scattering and absorption parallel to the plane for each medium (cloud, ocean, or aerosol layer) and optical properties assumed to be vertically inhomogeneous. A new radiative transfer (RT) method is proposed to deal with the variation of vertically inhomogeneous optical properties in the layers of a model for solar spectral radiation. This method uses the standard perturbation method to include the vertically inhomogeneous RT effects of cloud and snow. The accuracy of the new inhomogeneous RT solution is investigated systematically for both an idealized medium and realistic media of cloud and snow. For the idealized medium, the relative errors in reflection and absorption calculated by applying the homogeneous solution increase with optical depth and can exceed 20%. However, the relative errors when applying the inhomogeneous RT solution are limited to 4% in most cases. Observations show that stratocumulus clouds are vertically inhomogeneous. In the spectral band of 0.25-0.69 μm, the relative error in absorption with the inhomogeneous solution is 1.4% at most, but that with the homogeneous solution can be up to 7.4%. The effective radius of snow varies vertically. In the spectral band of 0.25-0.69 μm, the relative error in absorption with the homogeneous solution can be as much as 72% but is reduced to less than 40% by using the inhomogeneous solution. At the spectral wavelength of 0.94 μm, the results for reflection and absorption with the inhomogeneous solution are also more accurate than those with the homogeneous solution.