Mesoscale Energy Spectra of the Mei-Yu Front System. Part II: Moist Available Potential Energy Spectra

In Part II of this study, a new formulation of the spectral energy budget of moist available potential energy (MAPE) and kinetic energy is derived. Compared to previous formulations, there are three main improvements: (i) the Lorenz available potential energy is extended into a general moist atmosphere, (ii) the water vapor and hydrometeors are taken into account, and (iii) it is formulated in a nonhydrostatic framework. Using this formulation, the mesoscale MAPE spectra of the idealized mei-yu front system simulated in Part I are further analyzed. At the mature stage, the MAPE spectra in the upper troposphere and lower stratosphere also show a distinct spectral transition in the mesoscale: they develop an approximately −3 spectral slope for wavelengths longer than 400 km and − spectral slope for shorter wavelengths. In the upper troposphere, mesoscale MAPE is mainly deposited through latent heating and subsequently converted to other forms of energy at the same wavenumber. At wavelengths longer than roughly 400 km, the conversion of MAPE to horizontal kinetic energy (HKE) dominates, while at shorter wavelengths, the mechanical work produced by convective systems primarily adds to the potential energy of moist species and only secondarily generates HKE. However, this secondary conversion is enough to maintain the mesoscale − HKE spectral slope. Another positive contribution comes from the divergence term and the vertical flux. In the lower stratosphere, the main source of mesoscale MAPE is the conversion of HKE, although the vertical flux and the spectral transfer also have notable contributions.