Radiative Transfer in the Atmosphere

The mathematical and physical description of how radiant energy is absorbed, emitted and scattered as it travels through the atmosphere.

Definition

Radiative transfer is the process by which the intensity of electromagnetic radiation changes along a path through a medium that absorbs, emits and scatters it, governed by the radiative transfer equation.

Scope

Covers the radiative transfer equation and its solution under absorption, emission and multiple-scattering conditions; optical depth and extinction; Beer-Lambert attenuation; source functions and thermal emission; scattering phase functions; and approximations such as the two-stream and discrete-ordinate methods used in radiation models.

Core questions

• How does radiant intensity evolve along a path through an absorbing and scattering atmosphere?
• How are absorption, emission and scattering combined in a single transfer equation?
• What approximations make radiative transfer tractable in numerical models?

Key theories

The radiative transfer equation

A differential equation relating the change in radiant intensity along a path to losses from extinction and gains from thermal emission and in-scattering, parameterized by optical depth and the single-scattering albedo.

Mechanisms

Along an infinitesimal path, intensity is reduced by absorption and out-scattering (extinction, expressed through optical depth) and increased by thermal emission, which depends on the Planck function and local temperature, and by in-scattering of radiation from other directions described by the phase function. Solutions range from simple Beer-Lambert attenuation for absorbing media to multiple-scattering treatments such as discrete-ordinate and two-stream methods.

Clinical relevance

Radiative transfer codes are the engines of satellite remote sensing retrievals, weather and climate model radiation schemes, and atmospheric correction of imagery.

History

Building on Schwarzschild's early treatment of radiative equilibrium in stellar atmospheres, Chandrasekhar's 1950 monograph Radiative Transfer established the rigorous framework later adapted to planetary atmospheres and embedded in operational radiation models.

Key figures

• Subrahmanyan Chandrasekhar
• Kuo-Nan Liou

Seminal works

• chandrasekhar1960
• liou2002

Frequently asked questions

What is optical depth?

Optical depth is a dimensionless measure of how much a beam of radiation is attenuated along a path; an optical depth of one means the intensity is reduced by a factor of about 2.7 by extinction.