A method of evolving synoptic maps of the solar magnetic field

The evolution of magnetic flux at the solar surface is widely modeled by the flux transport equation. This describes the distribution of flux from instant to instant over the whole surface but does not describe how the synoptic map for one Carrington rotation evolves into the synoptic map for the next rotation. We derive the correct synoptic evolution equation, show that a simple version yields extremely accurate predictions of synoptic maps and discuss the implications for previous studies of the evolution of surface magnetic structures. We also note that the procedure yields a method of reconstructing an approximate map of the flux over the whole surface at any instant.