Invariance and Symmetry Methods in the Development of a Polarized CRTM

If applied correctly, symmetries and invariances can simplify the solution of various kinds of equations considerably. The purpose of this presentation is to provide an overview of symmetry and invariance properties of the radiative transfer equation impact the existing CRTM solver and can provide possible benefits for the development of a polarized CRTM. The most important symmetry group of the radiative transfer equation is its scaling symmetry. Not only does it provide the basis for the delta-M and delta-fit truncation methods for strongly peaked phase functions common in atmospheric applications, but also allows the construction of an efficient two-component solution method of the radiative transfer equation for such scenarios. Furthermore, it is discussed how the principle of invariance of radiative transfer, i.e. the invariance of the emergent radiation from a plane-parallel atmosphere to the addition of layers of arbitrary optical thickness relates to the doubling method used in the CRTM. Lastly, it is discussed how the reciprocity symmetry of polarized light can be applied to reduce the number of necessary computations.