I understand that ambient occlusion is a simplification of, or a partial solution to, global illumination. How this interacts with physically based rendering is less clear, however, as at face value ambient occlusion is creating light from nothing.
The domain for ambient occlusion at a given point is the hemisphere around the tangent plane to the surface at that point, and ambient occlusion is considered to be indirect lighting. However, if you narrow down that domain to the silhouette of an area light, you get direct lighting, which is already computed and occluded using a shadow map.
This gets confusing, since for sunlight, BOTH techniques are commonly used. How do you account for the energy transfer from direct sunlight to indirect sunlight (ambient light)? I'm assuming it's related somehow to the atmospheric scattering of a scene, because as a scene gets more overcast and less sunny, direct lighting is reduced while indirect lighting is increased.
So this means that lots of different scattering phenomena can contribute to ambient lighting: air, clouds, fog, water (for an underwater scene), and so on. How do you deal with all of this in a way that conserves light, or at the very least does not create extra light (losing light is more acceptable, in my humble opinion)?