Accurate computation of moist available potential energy with the Munkres algorithm

Abstract

The moist available potential energy (MAPE) of a domain of air is defined as the maximum amount of kinetic energy that can be released through reversible adiabatic motions of its air parcels. The MAPE can be calculated using a parcel‐moving algorithm that finds the minimum enthalpy state for a given set of thermodynamic assumptions. However, the parcel‐moving algorithms proposed previously do not always find the minimum enthalpy state. In this article, we apply the Munkres algorithm to find the exact minimum enthalpy state and compare this exact algorithm with four inexact algorithms, including a new divide‐and‐conquer algorithm. The divide‐and‐conquer algorithm performs well in practice, while being simpler and faster than the Munkres algorithm, and it is recommended for future calculation of MAPE when the exact result is not required. Keywords: Poisson Equation, Laplacian growth, Diffusion Field, analytic solution, ramified network, Golden ratio