Linear fog on transparent material

In my scene I have a large plane with a transparent material giving the effect of a clear water.

I added the fog effect in the lighting settings, set it to linear and it worked fine except that the fog is rendered on a plane which means that rotating the camera will change the visibility of distant objects.
I imported the image effects package added the global fog script to my camera, checked the use radial distance button, unchecked the fog effect in the lighting settings and now my fog is radial but it does not render anymore on my transparent water.
If I check both global fog script and the fog in the lighting settings, it seems like the two fogs (plane and radial) are superposing so fogged water render on a plane again. If anyone has a clue about how to render radial fog on transparent material it would be really great because its been a while I'm searching. I found a related thread here but it seems they are using exponential fog. Thanks!