Tropical cyclone (TC) potential intensity (PI) theory has a well known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI which nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels which determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

Simulations of solar radiation management (SRM) geoengineering using comprehensive general circulation models (GCM) show a residual surface warming at high latitudes. Previous work attributes this to the difference in forcing structure between the increase in greenhouse gases and the decrease in insolation, but this neglects the induced reduction in atmospheric energy transport. Here we show that the difference in vertical structure of temperature change between increasing CO2, decreasing insolation, and decreasing atmospheric energy transport is the dominant reason for the residual near-surface warming at high latitudes. A single column model (SCM) is used to decompose the high latitude temperature change, and shows the importance of the bottom-heavy temperature change from the CO2 increase in explaining the residual polar warming. This model hierarchy invites caution when attributing high latitude surface temperature changes to the lapse rate feedback, as various forcings and nonlocal processes affect the vertical structure of temperature change differently.