A simple tod.xml edit to make the chance of rain zero. Light clouds and overcast weather are still possible. The mod includes tracks from the standard edition, so the only classic tracks covered are Brands Hatch and Jerez.
It hasn't been tested whether you'll be kicked from online sessions with the replaced files, so, as always, it's probably a good idea to back up the original files.
Installation instructions: Simply unpack the archive in the F1 2013 main directory.