The Moist Available Energy of a Conditionally Unstable Atmosphere

Two simple methods for computing the moist available energy for cases in which the total number of parcels is fairly small are discussed. The first is a swapping routine that finds the reference state by exchanging parcels whenever the swap reduces the total enthalpy. However, it can be proved by contrived example that the swapping algorithm does not always find the true reference state. A second brute force routine actually examines all possible arrangements of the parcels and chooses the one with the smallest moist enthalpy. At present, both routines allow only horizontally homogeneous reference states. In an exploratory study, the swapping routine was used to find MAE and reference state for a time sequence of GATE soundings, all of which are conditionally unstable. In spot checks, the brute force routine always agreed with the swapper. Results show that in passing from the given state of the reference state the lowest three hundred mb of the atmosphere typically exchanges places with the 300 mb above it. The reference state then contains a dry warm layer near the surface, but a supersaturated but cool layer in the middle troposphere. The upper portion of the sounding is not modified in passing from the given state to the reference state.