Significant change over NxM distributions

I have 100 sets of data, each of which consists of ~ 15 distributions along time, I’ve attached a figure of 1 of these sets to hopefully clear up what I mean. The plot shows the 95% confidence intervals and quartiles for each distribution, the red dot and line are actually irrelevant for this particular statistical test.

I want to determine for each of these sets whether or not between any two distributions, there is a significant difference. I originally considered the Kolmogorov Smirnov test, but for a reason I can’t remember now (which is frustrating me and I’m sure frustrating you too), that isn’t applicable. I’ve been considering the z test as outlined here: http://homework.uoregon.edu/pub/class/es202/ztest.html but i’m not sure if it is the best approach.

I also want to somehow be able to quantify the amount of sets of data across the 100 that contain significant difference, but not sure on how to do that yet (any ideas for that are most welcome).

Thank you very much