Title: Assessment of algorithms for computing moist available potential energy,
Abstract: Atmospheric moist available potential energy (MAPE) has been traditionally
defined as the potential energy of a moist atmosphere relative to that of the
adiabatically sorted reference state defining a global potential energy
minimum. Finding such a reference state was recently shown to be a linear
assignment problem, and therefore exactly solvable. However, this is
computationally extremely expensive, so there has been 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 algorithms'
performance 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 overlooked
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 theoretical
expression linking MAPE to Convective Available Potential Energy (CAPE)
previously derived by Kerry Emanuel. 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 how to make
progress towards constructing a satisfactory moist APE theory for the
atmosphere. We also outline a method for vectorising the adiabatic lifting of
moist air parcels, which increases the computational efficiency of algorithms
for calculating MAPE, and could be used for other applications such as
convection schemes.