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Isaac Held has posted a blog article on what he calls "the fruit fly of climate models", i.e. a simple reference model to help understand conceptual behavior. It's a "a dry atmosphere, an ideal gas on a spherical rotating planet forced only by radiative fluxes — modeled as a simple relaxation of temperature to a “radiative equilibrium” that is a function of latitude and pressure — and a frictional force that relaxes the flow near the surface to zero (in the reference frame rotating with the surface)." This might be an interesting model to attempt if people become more ambitious to write fluid dynamics codes for Azimuth. I haven't read Held and Suarez so I don't know exactly how ambitious it really is. (Simpler models would be things like beta-plane approximations.)