The Moist Static Energy of a Convective Cloud Field, Evaluated at Cloud Edge, Equals the Tropospheric Mean Saturated Static Energy, Independent of Climate State

Large-scale integral constraints on cloud behaviors can be used to guide more detailed representations in present and future climates. We present theoretical arguments that the average value of the moist static energy evaluated at cloud edge is nearly equivalent to the bulk atmospheric value of the moist static energy evaluated at saturation. In numerical modeling of a large deep-convective cloud field, the equivalence holds independent of a 10 K range in sea surface temperature. The constraint also provides a simplified method for estimating the mean level of neutral buoyancy, which is observed numerically to scale linearly with the enthalpy of air evaluated at the sea surface.