Rainbows work from sunlight being refracted 42 degrees as it strikes a raindrop. The 42 degrees is significant, because rainbows won't form if the sun is higher than 42 degrees up in the sky.
That's why rainbows are more prevalent in the mornings and evenings -- the lower the sun is in the sky, the higher the rainbow's arc will be. At sunset, the top of the rainbow would be at its peak arc of 42 degrees above the horizon.
But in the summer in Seattle, the sun gets as high as 68 degrees above the horizon, meaning you won't see rainbows in Seattle at noon in the summer. However, they're possible all day in fall, winter and spring.
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