Analytical models for tropical CAPE

In global climate models, convective available potential energy (CAPE) increases rapidly with warming (by several percent per degree), and this increase in CAPE is blamed for future increases in the frequencies of severe weather and lightning. Despite the societal importance of CAPE, there has been no theory for it or its temperature dependence. This began to change in 2013, when Singh and O'Gorman argued that tropical CAPE could be calculated numerically using the zero-buoyancy plume model. In this presentation, I will show that the zero-buoyancy plume model can be integrated to give analytical expressions for CAPE that correctly predict its magnitude and temperature dependence. Assuming fixed relative humidity (RH) and precipitation efficiency (PE), the analytical expression for CAPE exhibits Clausius-Clapeyron (CC) scaling (increasing by roughly 7 percent per degree of surface warming) up to a critical surface temperature (about 310 K), at which CC scaling begins to fail. This failure of CC scaling is related to the super-CC scaling of stratospheric humidity. Assuming fixed RH and entrainment rate, a different analytical expression for CAPE can be derived, which also exhibits CC scaling. This expression, which is applicable to both Earth and Saturn's moon Titan, has a surprising feature: the latent enthalpy of the condensing gas (water vapor on Earth, methane gas on Titan) drops out of the CAPE equation entirely.