A Climatological Analysis of Moist Potential Vorticity

In the late 1990s to early 2000s, Wayne Schubert and his research group published papers on the equations necessary for numerical modeling the moist, cloudy, precipitating atmosphere. A main focus of these papers was to derive a generalization of the potential vorticity (PV) to a moist atmosphere so that the limiting case of a dry atmosphere simplifies exactly to Ertel's PV. According to model simulations, they noted that even though the formulation of moist processes in numerical models must be precise, the essential moist PV dynamics of tropical cyclones appear to be very similar to those of dry PV. Nonetheless, moist PV has not been investigated to assess its impact on global climate in large data sets, such as reanalyses like ERA-Interim, MERRA, or NCEP/NCAR reanalysis. Part of the reason for the dearth of research on moist PV in the climate context is that moist PV can be tedious to calculate and moisture, clouds, and precipitation processes in most reanalyses are not represented in a way that is consistent with the formulation of moist PV in the literature. More specifically, most reanalyses diagnose rain water content and ice water content rather than predict them.

In this study, we calculate moist PV in the new ERA5 reanalysis, which has six prognostic equations for clouds and precipitation, including prognostic equations for rain water content and ice water content. We discuss the differences between moist PV and dry PV in a large-scale context for an array of phenomena, including stratocumulus regions, the intertropical convergence zone, and tropical cyclogenesis. Also, we discuss the applicability of a concept that arises from moist PV invertibility that Wayne Schubert's research group called atmospheric "spice" in reference to a similar concept in oceanography. Lastly, we present a tool that can be used by the scientific community that diagnoses moist PV using either pressure or model level data, minimizing the tediousness of its calculations.