Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

TLDR

The authors present a general, fully documented discrete‑ordinate algorithm for time‑independent radiative transfer in vertically inhomogeneous, nonisothermal, plane‑parallel media. The method models thermal emission, scattering, absorption, and bidirectional reflection/emission, supports atmospheric applications from UV to radar, allows top‑boundary forcing, and is implemented in FORTRAN with user‑available code. The algorithm incorporates recent advances that eliminate two major ill‑conditioning problems—eigenvalue/eigenvector computation and matrix inversion for integration constants—yielding numerically stable solutions.

Abstract

We summarize an advanced, thoroughly documented, and quite general purpose discrete ordinate algorithm for time-independent transfer calculations in vertically inhomogeneous, nonisothermal, plane-parallel media. Atmospheric applications ranging from the UV to the radar region of the electromagnetic spectrum are possible. The physical processes included are thermal emission, scattering, absorption, and bidirectional reflection and emission at the lower boundary. The medium may be forced at the top boundary by parallel or diffuse radiation and by internal and boundary thermal sources as well. We provide a brief account of the theoretical basis as well as a discussion of the numerical implementation of the theory. The recent advances made by ourselves and our collaborators-advances in both formulation and numerical solution-are all incorporated in the algorithm. Prominent among these advances are the complete conquest of two illconditioning problems which afflicted all previous discrete ordinate implementations: (1) the computation of eigenvalues and eigenvectors and (2) the inversion of the matrix determining the constants of integration. Copies of the FORTRAN program on microcomputer diskettes are available for interested users.