A modified moist potential vorticity, its properties, and application

Abstract

[1] A modified moist potential vorticity (MMPV) and its tendency equation are derived in terms of modified potential temperature and the specific volume of dry air. MMPV holds not only the simplicity of virtual potential vorticity but also the conservation, impermeability, and invertibility principles of potential vorticity under certain conditions. More importantly, the effects of various nonconservative processes are explicitly included in its tendency equation. It can be seen from the MMPV tendency equation that contributions of moist species (water vapor and hydrometeors) to moist potential vorticity anomalies are twofolds: (i) the latent heating and the mass forcing of water vapor associated with moist microphysical processes and (ii) the solenoidal terms associated with the nonuniform distribution of moist species. Thus, we believe that it will be convenient to use MMPV in investigating the impact of diabatic processes and moist species gradients on the evolution of weather systems. A case study indicates that the MMPV does show strong signals aligned with the horizontal distribution of precipitation, suggesting its potential use as an accurate diagnostic variable. Since the MMPV tendency equation is derived from fully compressible and nonhydrostatic moist atmosphere system, the MMPV will also be a valid tool for evaluating and improving mesoscale numerical models such as the Advanced Research Weather Research and Forecasting model.

Understanding the vertical structure of potential vorticity in tropical depressions

“…; Peng et al . ). Perhaps most importantly, a complete theory would consider two‐way interactions between diabatic heating and PV.…”

“…Alternate forms of PV developed for moist, convecting atmospheres might also be useful (e.g. Schubert et al, 2001;Peng et al, 2013). Perhaps most importantly, a complete theory would consider two-way interactions between diabatic heating and PV.…”

A potential vorticity diagnostics package for MPAS-Atmosphere

“…However, other atmospheric PV quantities have been described in the literature that use thermodynamic variables that also encompass the effects of moisture, such as virtual potential temperature θ v , moist potential temperature θ m , and equivalent potential temperature θ e . As these "moist PV" quantities come in different flavors, they accordingly all have different properties, conservation laws, and inevitability principles (e.g., Cao & Cho, 1995;Kooloth et al, 2024;Marquet, 2014;Peng et al, 2013;Schubert et al, 2001). While extending the PV diagnostics package to some of these quantities is well beyond the scope of our efforts, the framework we have provided could be useful to those who may wish to incorporate a moist PV diagnostics package into MPAS-Atmosphere in the future, such as one utilizing the decoupled prognostic thermodynamic variable, θ m (Peng et al, 2013).…”