Get some sea 2 summit dry bags from a camping store and wrap them around the contents of your pannier/backpack. Seriously, I've ridden in some tropical downpours, and even the occasional flood and they've never failed me.
I've tried rain covers before and they just didn't work. All the water collected in the bottom of the cover after running down the inside of the pannier and soaked whatever I'd packed at the bottom.
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I am clinically insane. I am proud of it.
That is all.