Fog in post

Our scene has a minimal FG setting with a skylight in mental ray.

turn on enable filtering in Z Depth to get rid of jaggies

or ...  in Renderer tab, turn on fast rasterizer

Make a layer mask set to reveal all.

Reveal all reveals our image of the columns without hiding anything. If we selected "hide all" we would see only the white layer below.

[To dramatize the point, here is hide all selected:]

Add Z-depth to a mask using the alt key to activate the mask and paste it in directly.

You can see, wherever we have white within the mask, the image is "protected" and we can see it. Wherever we have black, it hides or "pokes through" the image so we see the white layer below.

Make a channel of render clouds and one for vertical falloff.

Load and delete the render clouds from your mask.

Whate we are doing here is, removing cloud shaped bits of the mask, resulting in less black in the mask ... so we see still less of the white layer below.

Load and delete the gradient.

This is to keep the fog from going up into the sky. By activating the channel, we are selecting the white area at the top ... deleting it, we see even less of the white below.

You can edit the mask if you want by using the alt key

Here is your composited fog: