  Convective available potential energy (CAPE), a metric associated with severe
weather, is expected to increase with warming. Under the most widely-accepted
theory, developed for strongly convective regimes, mean CAPE should rise
following the Clausius-Clapeyron (C-C) relationship at 6-7%/K. We show here
that although the magnitude of CAPE change in high-resolution model output is
only slightly underestimated with simple theories, it is insufficient to
describe the distributional changes, which has a down-sloping structure and is
crucial for impact assessment. A more appropriate framework for understanding
CAPE changes uses the tight correlation between CAPE and moist static energy
(MSE) surplus. Atmospheric profiles develop appreciable CAPE only when MSE
surplus becomes positive; beyond this point, CAPE increases as $\sim$25% of the
rise in MSE surplus. Because this relationship is robust across climate states,
changes in future CAPE distributions can be well-captured by a simple scaling
of present-day data using only three parameters.
