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Summons rain for five turns. If the user is holding the item Damp Rock, it lasts for eight turns instead. While in effect, it increases the damage of Water-type moves by 50%, and causes Fire-type moves to do half damage. Thunder always hits (and has a chance to hit through Detect and Protect equal to 100% minus the accuracy against a non-Protected opponent). SolarBeam has 60 Base Power. Moonlight, Morning Sun, and Synthesis heal 1/4 of the user's maximum HP. Pokémon with the Swift Swim ability have double Speed. Pokémon with the Forecast ability become Water-type. At the end of each turn, Pokémon with the Rain Dish ability heal 1/16 HP, Pokémon with the Dry Skin ability heal 1/8 HP, and Pokémon with the Hydration ability cure themselves of status ailments.
Smogon has an article on this topic.
Hail is an Ice-type equivalent.
Sandstorm is a Rock-type equivalent.
Sunny Day is a Fire-type equivalent.