# Why doesn't the sun reflect off Earth's oceans from space like a billiard ball?

According to Phil Plait, Earth is proportionally smoother than a billiard ball (http://blogs.discovermagazine.com/badastronomy/2008/09/08/ten-things-you-dont-know-about-the-earth).

The water surface should be much smoother. According to https://skeptics.stackexchange.com/questions/10763/is-earth-as-smooth-as-a-billiard-ball, 60-foot ocean waves correspond to 0.08 microns where a real ball's variation is in the order of 1 micron.

Why then isn't the reflection of the sun seen from space (http://www.esa.int/spaceinimages/Images/2014/07/Earth_glinting_in_the_sun) as specular as that off a billiard ball (http://www.diagnosisdiet.com/wp-content/uploads/2013/04/Billiard-Ball-2-licensed.jpg)?

## 2 Answers

The fact that the ocean is proportionally smooth doesn't matter -- when a light wave with wavelength ~500 nm hits the ocean, all it knows is that it's running into huge, 60 foot tall irregularities. It doesn't care if these waves are small compared to the rest of the earth. I mean, how would it even know?

For specular reflection, you need smoothless relative to the wavelength, not relative to something else.

• You might want to rephrase that. You need smoothness relative to the wavelength of light, not the size of the earth. – WhatRoughBeast Jul 16 '15 at 21:46
• Yeah, I guess I should have made that more explicit. The point is that "smooth relative to the Earth" is meaningless for light waves. – knzhou Jul 16 '15 at 21:49
• Yup, but "absolute smoothness" usually implies, well, absolute smoothness - that is, being perfectly smooth, when there are perfectly good optical standards for the allowable roughness of an optical surface. – WhatRoughBeast Jul 16 '15 at 21:51
• Oh, right. I forgot about that other meaning, I meant absolute as in 'not relative to X', not 'totally, 100%'. – knzhou Jul 17 '15 at 1:03
• This. The key point is that for "proportionally smooth" to be in any way relevant, you'd have to scale up the light waves, too. – Lightness Races with Monica Sep 26 '15 at 21:44

The billiard balls do not have atmosphere (O2,H2O, N2, CO2, O3, particulate, ...), clouds, forests, terrain, sea. Each component modulate the answer in relation to absorption, refraction and reflection, trapping/reflecting more or less radiation.

More heat from the sun at the surface >> more water vapor in the atmosphere >> more clouds >> more albedo (reflection) >> less heat at the surface.

The more or less smoothness is almost irrelevant because the particulate and the molecules in the atmosphere make the medium a dispersive one (the why the sky is blue instead of transparent) and the rays are less and less parallel one irt the others as they progress thru the atmosphere. Nevertheless a substantial part of the incoming radiation, the most of it or even more because of the internal heat of the Earth, is reflected back to space. I do not have present the actual thermodynamic budget and I will leave to others to say better and correct me if I'm more or less wrong.
As an answer to the question this should be enough.