I'm creating PDFs of rainfall observations, and I've got six years of data. I'm trying to see if small changes in some model parameters create PDFs that are significantly different than what I'd expect from interannual variability, which I'm representing by the six years of observations. I'm thinking of calculating the distance between the distributions, with perhaps an emphasis on "extreme values", defined to be greater than, say, 50 mm/day and seeing if the distance between two model PDFs (with two different sets of parameters) is greater than, say, the maximum distance between the observational PDFs. I've thought about using the 2-sample Kolmogorov-Smirnov test, but the test says that basically all of the six years are different from each other, and also I'm not sure if the yes/no nature of a hypothesis test is what I want to do here..I want more of a number. Also, given the nature of extreme rainfall, some years have (very rare) values that go out to about 2000 mm/day, while others only go to about 1000 mm/day..not sure if that will impact the metric used.
In the image the bold brown and magenta lines denote regions (southeast and west), but one could imagine that they arise from the two sets of model parameters, and that the spread between them is greater than that between the observations. What's a good way to quantify this difference?