Why do only tangential branches reflect? In this picture note that only the branches tangent to the light are lit up, so concentric circles of lit branches appear around the light:

I've noticed I similar effect with the peaks of water waves in a rainy puddle with a streetlight reflected in it. 
What process(es) underlie(s) this phenomenon?
 A: That's because only tangential branches have a surface properly angled with respect to the moon and the objective to offer reflection.
You can take a torch light and a toilet paper core - or any other cylinder shaped object to simulate the shape of the branches- wrapped in aluminium foil to do this at home
A: It's actually pretty intuitive:
Take a branch segment, first of a branch pointing entirely radially outwards, say placed below the light source.
The part of the branch segment that would reflect light, the top section, is covered by the rest of the branch, therefore no reflection!
Now take that branch segment to be tangential (still below the source). The portion that could reflect, the top, is entirely revealed, since the branch now runs right-left, so it reflects the maximum amount of light.
We can interpolate that at intermediate angles, intermediate amounts of light will be reflected.
To reiterate a main point, the more tangential a branch is, the more  it reflects, so we see an overall tangential orientation across all branches. We notice the brighter ones more, and the brighter ones are more tangential.
Notice that not all lit branches are precisely tangential in the picture, but the overall "impression" is a tangential orientation.
So, we see hints of concentric circles!
I assume the same argument applies to the peaks of water waves etc.
