Start with "Dear Rain" because it's respectful, then be self-effacing right off the bat.
"I know I'm an asshole for going back and forth about you." that way the rain won't want to call you an asshole because you already came up with it.
Get hostile all of a sudden. "But seriously, who gives a shit what you think of me? You're weather." That was cold but it's the only way to guarantee a clean break.
Now it's time to lay it all down plain. "On Monday I was into you. On Tuesday, I thought, this is still kind of boss. Today, sorry but you're what's wrong, not me."
You're doing it! You're really doing it! Keep going. "I probably didn't need to write this letter because I see according to a website that can see into the future that tomorrow you're going to be replaced by sunshine and also you can't read (no eyes)."
Ouch on the 'no eyes' thing.
"Bye and once more, I don't like you the way I did 40 hours ago (that was fun then)."
Awesome. Now close. "So long. Love (why did I write love, I don't), [your name]."
Yes! That rain is going to kill itself you broke its heart so sad.
Happy Write A Letter To Some Rain Day!