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Radiative transfer (also called radiation transport) is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative transfer describes these interactions mathematically. Equations of ...
The radiative transfer equation is a monochromatic equation to calculate radiance in a single layer of the Earth's atmosphere. To calculate the radiance for a spectral region with a finite width (e.g., to estimate the Earth's energy budget or simulate an instrument response), one has to integrate this over a band of frequencies (or wavelengths).
The RTE is a differential equation describing radiance (, ^,).It can be derived via conservation of energy.Briefly, the RTE states that a beam of light loses energy through divergence and extinction (including both absorption and scattering away from the beam) and gains energy from light sources in the medium and scattering directed towards the beam.
The radiation field thereby maintains the blackbody intensity appropriate for the local temperature. At equilibrium, I λ = B λ (T) and therefore dI λ = 0 even when the density of the GHG (n) increases. This has led some to falsely believe that Schwarzschild's equation predicts no radiative forcing at wavelengths where absorption is "saturated".
The method of discrete ordinates, or the S n method, is one way to approximately solve the RTE by discretizing both the xyz-domain and the angular variables that specify the direction of radiation. The methods were developed by Subrahmanyan Chandrasekhar when he was working on radiative transfer.
Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-matter interaction and the angles of deflection in a photon's trajectory when a scattering event occurs.
Putting this into the equation for radiative transfer we get = where s is the distance measured along the path traveled by the beam. The minus sign on the left hand side shows that the intensity decreases as the beam travels, due to the absorption of photons.
The grey atmosphere (or gray) is a useful set of approximations made for radiative transfer applications in studies of stellar atmospheres (atmospheres of stars) based on the simplified notion that the absorption coefficient of matter within a star's atmosphere is constant—that is, unchanging—for all frequencies of the star's incident radiation.