The role of criticality on the horizontal and vertical scales of 1 extratropical eddies in a dry GCM

4 This paper discusses the sensitivity of the horizontal and vertical scales of extratropical 5 eddies when criticality is varied in a dry, primitive equation, general circulation model. 6 Criticality is a measure of extratropical isentropic slope and when defined appropriately 7 its value is often close to one for Earth’s climate. The model is forced by a Newtonian 8 relaxation of temperature to a prescribed temperature profile, and criticality is increased by 9 increasing the thermal relaxation rate on the mean flow. When criticality varies near one, it 10 is shown that there exists a weakly nonlinear regime in which the eddy scale increases with 11 criticality without involving an inverse cascade, while at the same time the Rossby radius 12 may in fact decrease. The quasi-geostrophic instability of Charney problem is revisited. It is 13 demonstrated that both the horizontal and vertical scales of the most unstable wave depend 14 on criticality, and simple estimates for the two scales are obtained. We reconcile the opposite 15 trends of the eddy scale and Rossby radius and obtain an estimate for the eddy scale in terms 16 of the Rossby radius and criticality that is broadly consistent with simulations. 17