With the huge differences in the Northern and Southern Hemispheres temperature wise and roughness wise there are all sorts of interesting dynamics which somewhere along the line have to conserve angular momentum. During my brief foray into the PETM situation and the indications that sea levels might be hundreds of meters higher than today I wondered how you would have to model potential variation in Earth's rotation velocity to see if it was worth considering.
This dissertation, The Earth’s Atmospheric Angular Momentum Budget and its Representation in Reanalysis Observation Datasets and Climate Models by Simon Driscol at the University of Reading popped up. I haven't digested it all yet, but there is a mention of raising the lids on Hadley Center climate models to roughly 85 km from 40 km which was interesting. Since climate models basically suck at emulating most of the common "oscillations" and some even get reversed flows for know ocean currents, it is pretty obvious that they have had some issues with what should be very basic physics. Granted, modeling climate is a monumental task but not even coming close matching the difference between hemispheres to the point that they don't even want to discuss the differences between the hemisphere is pretty sad.
This is the second dissertation from the University of Reading that has caught my eye, the other being Andrew Barrett's recommended changes to liquid top cloud parameterization entitled, "Why can't models simulate mixed-phase clouds correctly." Barrett's conclusion was that properly parameterizing mixed-phase clouds could reduce modeled sensitivity to about 1.6 C per doubling which is right in line with most current estimates. I haven't followed up on how well is dissertation was received, but mixed-phase clouds was one of my pet peeves since increased relative humidity should impact the types of clouds being formed. This peeve goes all the way back to the issues with the Kiehl and Trenberth etc. Earth Energy Budget incorrect assumptions about the atmospheric window from the "real" surface when their assumption actually was for the top of the atmospheric boundary layer "surface".
So I might just have a bit more reading ahead of me. Both of these get into more intensive modeling that I am willing to pursue but worth a look.