Bows of rain

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It was another of those odd weather nights - it was raining yet the sun was shining, and all was aglitter as the sun sparkled off all of those tiny little liquid mirrors. And then I saw it, as I'd hoped that I would, that tall band of colour reaching from earth to sky in a defined arc.

And that got me to wondering: Are there rainbows in Middle Earth? If so, are these occasions where Varda is flirting with Ulmo, or some trisection of Varda, Manwë and Ulmo? Are they used as signs from above, as in Moses' Book of Genesis where God uses the rainbow to signify his promise not to flood the earth again? If rainbows happen, what, in Middle Earth, does a rainbow mean?

Are they simply for the beauty of it all, as another snub to Melkor, or is there a pot of Dwarven gold at the spot each touches the ground?