The hemispherical harmonic method for radiative transfer in plane-parallel atmospheres

Abstract

Abstract A new approach - Hemispherical Harmonic Method (HSHM) is proposed for radiative transfer in plane-parallel atmospheres and a prototype model is developed. The algorithm is derived from the unified formulation with the shifted Legendre polynomials prescribed as the basis functions decomposing the Fourier components of radiance and the radiative transfer equation. The solutions to the decomposed equations for homogenous layers and the inhomogeneous atmosphere-surface system are derived and numerically implemented. The primary numerical experiments show the prototype model gives accurate results when the order is sufficiently high, and has reasonable accuracy and efficiency relative to its discrete ordinate method (DOM) counterpart does with the same orders, including the numbers of the basis functions, the Fourier components, and the expansion terms of the scattering phase function. The HSHM model allows more flexible settings to further improve the accuracy and/or the efficiency. The method is inherently immune to the singularity problems suffered by the DOM for the special solar zenith angles. While further refinement is to be done, the HSHM provides another option for the modeling and remote sensing studies involving radiance and irradiance in planetary atmospheres with radiative absorption, scattering, and emission.