Is there a way to determine the quality of an impulse-response relationship?
I don't yet see the connection of your input with "impulses" in that if I understand correctly you are looking at the settled state from prior changes rather than dynamic responses. What you are asking for I believe is a statistical correlation between "Stream Flow" and "Stream Height"; given a stream flow (in the steady state), what is the "settled" stream height that would be sustained by that flow. I would argue that to be a correlation problem to the degree you are looking for a linear relationship between the two. We have other posts that detail how to compute the correlation coefficient, if you need further info on that you could look here:

Noise detection