I'm working on a simple airplane game where I use skybox cube rendered using disabled depth test.
Very close to the bottom side of the skybox is my terrain model.

What bothers me is that the terrain is not connected to the skybox bottom. This is not visible while the plane flies low, but as it gets some altitude, the terrain looks smaller because of the perspective. Since the skybox center is always same as the camera position, the skybox moves with the plane, but the terrain goes into the distance.

Ok, I think you understand the problem. My question is how to fix it.
It's an airplane game so limiting max altitude is not possible. I thought about some way to stretch terrain to always cover whole bottom side of the skybox cube, but that doesn't feel right and I don't even know how would I calculate new terrain dimensions every frame.

Here are some screenshot of games where you can clearly see the problem:
(oops, I cannot post images yet)

• darker brown is the skybox bottom here: http://i.stack.imgur.com/iMsAf.png
• untextured brown is the skybox bottom here: http://i.stack.imgur.com/9oZr7.png