Living at the Edge: At the Interface between Cloudy and Clear Skies, the Saturated Static Energy and Total Surface Area Have a Predictable Response to Climate Warming

Studies of how clouds will respond to a warming climate tend to focus on cloud areas, their heights and their temperatures. Here we show through a combination of numerical arguments, satellite observations, and detailed numerical simulations that the problem can be substantially simplified with a switch in coordinate system to one of cloud perimeter and the saturated static energy (SSE). We find that the value of the SSE at cloud edge is equivalent to, and scales linearly with, the volume mean SSE of the tropospheric domain - including clouds and clear skies. Specifically, as the density-weighted tropospheric mean value of the SSE (normalized by the specific heat of air) increased from 295 K to 305 K, so does the density-weighted value of the SSE evaluated at cloud edge. Going further, continuity constraints on the motions of air about cloud edge lead to a simple analytical expression for the number distribution of clouds with respect to the cloud perimeter and the deviation of the cloud edge SSE from the tropospheric mean value of the SSE. The derivation agrees closely with detailed numerical simulations and satellite observations. Importantly, the derivation requires knowledge only of tropospheric moist static stability and not of such considerations as aerosol concentrations, microphysical parameterizations, Coriolis forces, season, or whether clouds are over land or ocean. Indeed, the theoretical expectation that cloud perimeter distributions follow a power-law distribution with an exponent close to unity is reproduced closely in satellite imagery, and assuming a sufficiently large domain, the exponent is nearly the same wherever or whenever one looks. Such thermodynamic constraints may offer guidance for evaluating the performance of detailed global cloud resolving models representing a warmer Earth.