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Equations of radiative transfer have application in a wide variety of subjects including optics, astrophysics, atmospheric science, and remote sensing. Analytic solutions to the radiative transfer equation (RTE) exist for simple cases but for more realistic media, with complex multiple scattering effects, numerical methods are required.
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".
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.
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.
The Diffusion Theory is an approximation of the radiative transfer equation (RTE), and an analytical way to simulate photon transport. As such, it has the ability to model photon propagation through tissue quickly.
Radiation trapping, imprisonment of resonance radiation, radiative transfer of spectral lines, line transfer or radiation diffusion is a phenomenon in physics whereby radiation may be "trapped" in a system as it is emitted by one atom and absorbed by another.