Do waterfalls generate pink (1/f) or brownian (1/f^2) noise?
Interesting question. I juts happen to live right outside a waterfall so I can relate some hands on experience.


The sound depends A LOT and water flow and weather conditions. Water flow is the main engine but wind can generate significant modulations
Depending on conditions you can get strong harmonics in the signal. Sometimes you can actually see standing waves running up and down the fall. These tend to be very low in frequency: maybe around 1 Hz or so.
The fall is pretty wide and has strong directivity. So the spectrum heavily depends where you are.
Overall it sounds more brown than pink
Fun fact: if the fall hits the right resonance, it noticeably shakes the house and the dishes in the kitchen cabinet start to rattle.


This is just for one specific fall and I'm sure others behave quite differently. So all in all any simple model would be a gross over-simplification.