Probability Density Functions to Represent Magnetic Fields at the Solar Surface

Numerical simulations of magneto-convection and analysis of solar magnetogram data provide empirical probability density functions (PDFs) for the line-of-sight component of the magnetic field. In this paper, we theoretically explore effects of several types of PDFs on polarized Zeeman line formation. We also propose composite PDFs to account for randomness in both field strength and orientation. Such PDFs can possibly mimic random fields at the solar surface.