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I think water is still blue as the color is a property of what is dissolved in it and from my experience in a overcast situation I remember it is still blue underwater
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IIRC the colour of the water, both the surface and below, is due to the sky above it (Thus the grey water when the weather is overcast) in deep water areas, and the colour of the bottom in shallow depth areas. The mediterranean looks more "turquoise" because the bottom is a mix of brownish-orange rocks and yellow sand. The Artic looks pale blue in shallow water because of the lots of ice, and very deep blue in deep water areas because of the dark (volcanic) rocks of the bottom/coast.
The sky itself is blue because of the degradation of the black space (cosmos) when seen through layers of air and everything floating in the atmosphere.
BUt I could be wrong ... must check this all
EDIT: Found the answer, yes it was right:
http://www.sciencemadesimple.com/sky_blue.html