A note about Splash Mountain if you want to stay dryer (do the opposite if you want to get wet).
Check the seat before you sit down (depending on where the people in the boat before you were sitting the seat may be wet).
Keep your feet up (easiest if you sit in the front of the boat). Water can collect in the bottom and will move around as you go up and down the hills. It's easy to end up with very wet socks.
Ride in the lightest boat possible. More weight means the boat sits lower in the water and hits the bottom of the drops with a greater force displacing more water, some of which will end up on you.
Sit in the front of the boat. Just before the boat hits the bottom of the drop, duck forward pulling your head down towards your chest and make sure your arms are in. Only your back is exposed, so only that will get wet. Be warned though, all the water that would have gone on you will end up on the person behind you (Mom won't let me sit in front of her anymore).
For Kali River Rapids, be prepared to get soaked. I've always just sorta gotten wet, but have seen people soaked. Lighter boats seem to do a little better at staying dry, but not always. All depends on whether you get stuck under the water fall and how you hit that last hill and short of some high powered analysis with super computers and probably some chaos theory, there's no way to figure that one out.
The other option is to wear rain gear on the water rides. You might look a little silly, but you'll be dry (and the afore mentioned Mom won't be. But, she's a good sport.

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