I am looking at Arctic ice thickness from two different Earth-orbiting satellites A and B. I'm interested in quantifying how well these two datasets agree, but I'm struggling over what parameters to use.
I have plotted the data below.
(a) shows the histograms of thickness from A (blue) and B (red).
(b) shows the difference (B minus A) at each location.
(c) shows a scatter plot of thickness from satellite A vs. thickness from satellite B. I have plotted the first principal component in dashed blue, which shows the primary trend in the data. The equation of this line is y= 0.991 x + 0.024
From this comparison I want to extract two quantities:
1) The 'average' difference in thickness between A and B
Looks by eye to be ~ 2 cms
2) The 'goodness' of the correlation.
As a starting point, maybe I need advice on how to fit a PDF to a histogram that is not Gaussian, when I do not know what kind of distribution it is. Other studies tell me that ice thickness is log-normal, but I have values below zero which contradicts this idea (I think)
Any help on this appreciated. It's easy to eye-ball that these two datasets agree 'quite well' but are off by 'a few cms', but I need numbers!