radiationmodels

Radiation models are mathematical frameworks used to describe the propagation of electromagnetic radiation through and between media. They are employed to predict radiative energy exchange in fields such as atmospheric science, astrophysics, engineering, and computer graphics. A central component is the radiative transfer equation, which tracks the change in specific intensity along a path due to emission, absorption, and scattering by matter. Solutions require approximations or numerical methods, resulting in categories such as gray models, spectral (nongray) models, and multi-band approaches.

Common solution strategies include the diffusion approximation (a low-transport-mean-free-path limit), the two-stream or discrete ordinates method (SN), spherical harmonics (PN), and Monte Carlo or ray-tracing simulations. In computer graphics, radiosity, path tracing, and photon mapping are used for global illumination. In engineering and climate studies, models parameterize spectral properties through emissivity, absorptivity, scattering coefficients, and phase functions, often with k-distribution or line-by-line treatments to represent gas absorption, and use view factors or surface properties to compute radiative exchange between surfaces.

Key inputs include geometry, spectra of sources, optical properties of media, and boundary conditions. Model choice balances accuracy and computational cost, with gray or diffusion-based models offering speed, and high-fidelity line-by-line or Monte Carlo approaches offering detail. Validation relies on benchmark problems and comparison to measurements.

Radiation models are essential for designing thermal systems, interpreting planetary atmospheres, simulating light transport in scenes, and modeling energy budgets in climate systems.