Hydrology by residence, travel and exit times: disentangling notation and concepts

I was always convinced that looking at water budgets by residence times gives an interesting a different perspective. But my approach, so far, was mainly connected to the GIUH approach, and, in particular, to the GIUH determined from the width functions. Whilst this was fruitful with some interesting results and insights, I am kind of naive with respect to the recent work promoted by Gianluca Botter, Andrea Rinaldo, Enrico Bertuzzo and coworkers.
So together with Marialaura Bancheri, I dove in some of the papers of my friends, trying  to select, at the moment, those features related to the water budget. The result, so far, is the presentation you see below, by clicking on the image.

It does not escape to my attention that this is just a little part of the story. But, for the moment, it is enough, and this will bring certainly to new components for the JGrass-NewAGE system. Please, for some bibliography, see this previous post.