Principles of Radiative Transfer

Abstract

The article gives an introduction to classical vector radiative transfer theory (RTT). It comprises a brief summary of the fundamental quantities in RTT and the corresponding definitions. Based on these quantities, the transfer equation for radiation will be introduced in its basic form for a plane-parallel, horizontally homogeneous atmosphere. Polarization and the Stokes vector are introduced, which extend the scalar radiative transfer equation to the more general form of the vector radiative transfer equation. Scattering processes and interactions with the surface are discussed within the mathematical framework given in the first part of the paper. As an example, the theoretical concept presented is then applied to passive microwave remote sensing. A solution for the radiative transfer equation, which is commonly used for the retrieval of atmospheric quantities (e.g. water vapor) and land surface properties (e.g. soil moisture), is derived based on approximations and simplifications. More general approaches to solve the radiative transfer equation including multiple scattering are described and discussed in a separate section.

Submillimeter Wave Instrument radiometry of the Jovian icy moons

“…If the sources f (τ) are isotropic and nonpolarized, the third and fourth Stokes parameters of the radiance field (U and V) vanish due to the rotational symmetry of the VRTE solution, and so the resulting scattering matrix is effectively a 2 × 2 matrix and the VRTE solution is the angular distribution of the twocomponent Stokes vector with the I, Q components (Drusch & Crewell 2005).…”

“…is the Planck black body radiation function (Janssen 1993;Drusch & Crewell 2005), h and k B are the Planck and Boltzmann constants, respectively, and ν is the frequency. If the quantum energy at the radiation frequency is small compared to the temperature ω kT , the Planck function is almost proportional to the temperature (the so-called Rayleigh-Jeans approximations):…”