When leaving ground effect, why is there a nose-up change in moment?
The aerodynamic centre of a wing shifts when it is in ground effect. Out of ground effect, the wing produces lift by accelerating air downwards. In ground effect the ground prevents the air from being deflected downwards, and more lift is produced due to increased pressure underneath the wing. This pressure has a different distribution than out-of-ground effect pressure, hence the change in pitching moment.

Consider a cross section of a wing: free stream lifting force centre is at the quarter chord point. If the wing was supported by just static pressure only, like a hovercraft, the force centre point would be at 50% chord.


  Actually not sure now if the horizontal tail has much influence but
  I'll leave the original answer underneath:


Ground effect works by increasing static pressure underneath the wing and the horizontal tail. The aircraft flies out of ground effect in a nose-up attitude, and depending on tail configuration it can be possible for the main wing to be out of ground effect while the horizontal tail still experiences increased pressure underneath, therefore creating a nose-down pitching moment. Once the horizontal tail flies out of ground effect as well, the nose-down pitching moment disappears. I would not expect that T-tails have this change in pitching moment but I have never flown one.