How to darken a procedurally added texture (explained below)

The terrain within my 2D game is procedurally generated using mid-point displacement. As displayed below, the terrain is generated as a mesh and a texture is applied to it (this can be seen in the blue terrain in the image below).

The result I am hoping for is seen in the following picture. I want to darken this terrain below a certain point below the main height-map of the terrain, to make it smoothly fade to black.

I have no idea how to achieve this effect on a procedural terrain (differing heightmap created in each level). Was hoping someone could point me in the right direction.

Thanks in advance!