Several types of divination are related to the observation of weather:
Aeromancy includes several types of air-related divinations, and was one of seven forbidden types of magic in renaissance Europe. Aeromancy had several subtypes, austromancy (wind divination) and ceraunoscopy (thunder and lightning divination).
Solarmancy: divination based on the sun.
Hydatomancy: divination based on rainwater.
Nephomancy: divination based on cloud formations.