The surface of the choppy water acts as a diffuse reflector.
Work Step by Step
As Figure 23-4a illustrates, diffuse/specular reflection from a rough surface bounces every which way. At practically every location in the water between you and the moon, there is some facet of the water surface that reflects the light to you. If the water were even choppier, the column of light would become wider. If the water surface were as smooth as a mirror, you would see an image of the round moon on the surface of the water.