Positively homogeneous functions in atmospheric radiative transfer theory (Q624620)

Positively homogeneous functions are applied to describe absorption and scattering processes within the framework of atmospheric radiative transfer theory. Solid angle integrations are understood as surface integrations over arbitrary solid angle surfaces which are defined beyond the common picture of atmospheric radiative transfer. It is shown that for three different classes of functions describing radiative transfer quantities and radiances, that means so-called ray functions (RF: functions constant along each ray) normalized direction density functions (NDD: normalized functions dependent on the radiation direction), and square-dependent direction density functions (SDD: functions decreasing quadratically in the radiation direction), different solid angle integrations, which are invariant under change of certain solid angle surfaces, exist.