Day Night Cycle sun fade

Ive made a day night cycle with a sun and a moon with a script I've called GameTime to govern how they move and the blending skybox. When the main sun sets, however, it's light seems to shine through the terrain and still effect all my game objects by making them light up on the bottom, EG: the foliage on the trees still lights up according to the sun as it travels underneath my terrain. Is there some way to cause my sun to fade once it has set and the regain intensity as it rises again?