Assessment of algorithms for computing moist available potential energy

Atmospheric moist available potential energy (MAPE) has traditionally been defined as the potential energy of a moist atmosphere relative to that of the adiabatically sorted reference state defining a global potential energy minimum. Although the Munkres algorithm can in principle find such a reference state exactly, its computational cost has prompted much interest in developing heuristic methods for computing MAPE in practice. Comparisons of the accuracy of such approximate algorithms have so far been limited to a small number of test cases; this work provides an assessment of the performance of the algorithms across a wide range of atmospheric soundings, in two different locations. We determine that the divide‐and‐conquer algorithm is the best suited to practical application, but suffers from the previously unexplored shortcoming that it can produce a reference state with higher potential energy than the actual state, resulting in a negative value of MAPE. Additionally, we show that it is possible to construct an algorithm exploiting a previously derived theoretical expression linking MAPE to Convective Available Potential Energy (CAPE). This approach has a similar accuracy to existing approximate sorting algorithms, whilst providing greater insight into the physical source of MAPE. In light of these results, we discuss possible ways to improve on the construction of Available Potential Energy (APE) theory for a moist atmosphere. Moist Available Potential Energy (MAPE) describes the energy available to atmospheric motion by taking the difference between the total potential energies (TPE) of the actual atmospheric state and a reference state. Reference states have previously been computed using sorting algorithms that approximate the reversible adiabatic rearrangement minimizing the TPE. However, we show that these algorithms regularly produce a reference state with even higher TPE than the actual state and therefore alternative approaches not based on sorting parcels are physically preferable.