The radio altimteter was designed as a landing aid, and has been adapted for uses beyond, such as GPWS. The signal bounced from the ground gets weaker with the square of the distance, so funny things can happen.
Just to be pedantic (I couldn't sleep a couple of nights ago and cracked open a textbook on radar), the signal gets weaker with the 4th power of distance, not the square. It turns out that the signal from the plane falls off with the square of the distance, as you'd expect, but in addition to that, the return also falls off with the square of the distance, causing an overall loss proportional to the 4th power of distance.
Which, of course, makes your comment all the more relevent.
