AddingDoublingRT
AddingDoublingRT (adrt) is an implementation of the adding–doubling
method for solving the radiative transfer equation in plane-parallel,
scattering, absorbing, and thermally emitting atmospheres. It is based on the
matrix operator method of Plass, Hansen & Kattawar (1973) with the
inhomogeneous-source and delta-M extensions of Wiscombe (1975, 1976, 1977).
The solver computes hemispheric fluxes, the actinic mean intensity, the net flux divergence (heating rate), the attenuated direct solar beam, and — for thermal problems — the analytic temperature Jacobians of all of these quantities.
Three interchangeable backends share a common configuration model and produce identical results:
C++ (CPU) — template-optimised kernels for \(N = 2, 4, 8, 16, 32\) quadrature streams with a dynamic fallback for arbitrary \(N\).
CUDA (GPU) — a batched solver that processes every wavenumber of a spectrum in parallel, one thread per wavenumber.
JAX (CPU/GPU) — a pure-Python implementation that is fully JIT-compiled, vectorised across wavenumbers, and differentiable through
jax.grad().
Note
This documentation covers the physics and mathematics of the method (Theory), how to drive the solver (User guide), the three backends and their APIs (Backends & API reference), and the source references (References). If you are new to the code, start with Quick start.
Feature overview
Thermal emission with a linear-in-optical-depth Planck source (Wiscombe 1976).
A collimated solar/stellar beam tracked separately through the doubling and adding steps, with direct-beam attenuation and diffuse scattering.
Combined thermal + solar sources in a single solve.
Delta-M scaling (Wiscombe 1977) for strongly forward-peaked phase functions.
A Lambertian surface with configurable albedo and thermal emission, or a diffusion-approximation lower boundary for optically thick stellar atmospheres.
Built-in phase functions — isotropic, Rayleigh, Henyey–Greenstein, double Henyey–Greenstein — or arbitrary Legendre moments.
Analytic temperature Jacobians of the fluxes, mean intensity, and heating rate (C++ backend), computed by reusing the forward operators.
Getting started
User guide
Theory
Appendix