In feeling that Hydrology needs new mathematical-physics, I explored several directions (Information Theory, Statistics, Causality theory, Algebraic topology, Thermodynamics -!-, and not very much the usual paraphernalia that modern physics uses whose taste I kind think to know, Petri Nets) and I arrived to category theory. Category theory is the mathematics of connections and retro-actions represented in graphical form. I arrived here because I think that expanding hydrology to Earth System Science, it opens to the world of connections, and understanding connections means understanding complexity.
For other definitions, please give a look to this new book by
Just at the first pages, it also address to other books, and I also found
I collected many other books and papers about CT. However, if you want to start, start from these two. Eventually you can subscribe to the Azimuth forum and enroll John Baez course.