Radiative transfer equation

The radiative transfer equation tracks how radiation intensity changes along a path through matter because of emission, absorption, and scattering.

Specific intensity: Radiant energy crossing a unit area, per unit time, solid angle, and frequency or wavelength. The equation evolves this directional quantity along each ray.
Optical depth: A dimensionless measure of cumulative extinction along a path through a medium. It replaces physical distance with a measure of accumulated attenuation.
Atmospheric radiative transfer: The transport of solar and terrestrial radiation through gases, clouds, and aerosols in an atmosphere. It applies the equation to weather, climate, and remote-sensing calculations.
Beer–Lambert law: A law stating that light attenuates exponentially with absorber concentration and path length in a nonemitting, nonscattering medium. It is a limiting attenuation model without the equation’s emission and scattering contributions.
Radiative transfer equation of a plane-parallel atmosphere: A one-dimensional radiative transfer equation for a horizontally uniform atmosphere stratified by height. This common geometry reduces the equation to depth and direction.
Solid angle: A dimensionless measure of the angular extent of a direction or region of a sphere. Radiation intensity and scattering are resolved over directions in solid angle.
Radiative transfer in stars: The transport of radiation through stellar interiors and atmospheres, shaping energy flow and emergent spectra. Stellar structure and observed spectra depend on how radiation escapes matter.
Diffusion approximation: An approximation that treats radiation as nearly isotropic and describes its net transport by a diffusion-like equation. It simplifies transport when repeated scattering makes radiation nearly isotropic.
Absorption coefficient: A measure of how strongly a medium removes radiation from a beam per unit path length. Absorption appears as a loss term proportional to intensity.
Extinction coefficient: The coefficient describing removal of radiation from a beam by absorption and scattering. It combines the two processes that attenuate the incident direction.

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