In my day job one of the courses I teach is statistical estimation. A key part of that isn't just parameter estimation -- there's also estimating "fit" or error from fit. There are analytical ways to assess goodness of fit but for this particular estimation problem, matching elevation profiles turns out to be a good way to evaluate areas and sources of fit and misfit. It turns out that many kinds of errors manifest in typically characteristic ways so you can often "see" what went wrong, where it went wrong, and the magnitude of the deviation. That turned out to be pretty cool. I wish more of my estimation problems were as cool.