The systematic representation of models in steps, or hierarchies, can help connect our understanding from idealized systems to comprehensive models, and ultimately, the Earth system in all its beauty and complexity. As pointed out by Isaac Held, the biological sciences have benefited greatly from the hierarchy of organisms provided by nature. The humble fruit fly can tell us much about the human being, but allows multiple groups to concentrate and understand one simpler system in detail, before we tackle ourselves. Our field, however, lacks a natural hierarchy of systems (excepting perhaps our neighboring planets, moons, and exoplanets, where observations are a real challenge), leaving us to build our own hierarchies. This puts us in a dangerous position where it is easy to make vague statements about the benefits of a model hierarchy (as in the introduction to many a proposal), but hard to pin down the intermediate models that truly deserve a unified focus across the field. In this talk, I’ll highlight an example of a model of intermediate complexity (a so-called dry dynamical core, essentially, a primitive equation solver on the sphere, with very simple “atmospheric physics”) that allowed us to solve a puzzle: the response of the stratospheric overturning circulation to anthropogenic forcing. My goal will be to give you a quick introduction to the physics of the problem (and why they are important for surface climate), and make a case that intermediate models can truly form a bridge between our fundamental understanding of the atmospheric circulation and our ability (or lack thereof) to simulate it with our most advanced prediction systems.