On the definition of a moist-air potential vorticity

Abstract

A new potential vorticity is derived by using a specific entropy formulation expressed in terms of a moist-air entropy potential temperature. The new formulation is compared with Ertel's version and with others based on virtual and equivalent potential temperatures. The new potential vorticity is subject to conservative properties ensured by the Second Law applied to the moist-air material derivatives. It is shown that the upper tropospheric and stratospheric (dry) structures are nearly the same as those obtained with Ertel's component. Moreover, new structures are observed in the low troposphere, with negative values associated with moist frontal regions. The negative values are observed in the frontal regions where slantwise convection instabilities may take place, but they are smaller than those observed with the equivalent potential vorticity. The main purpose of the article is to diagnose the behaviour of the new potential vorticity from numerical output generated by the ARPEGE NWP model, with the help of isobaric charts and vertical cross-sections. Two inversion methods are suggested. The first method could be based on the invertibility principle verified by the virtual potential vorticity, with a possibility to control and modify separately potential vorticity components in the (dry) upper and (moist) lower atmospheric levels. The other method may consist of an inversion process directly applied to the new moist-air entropy potential vorticity, because the negative values and the solenoidal term are smaller than those observed with equivalent potential vorticity, as shown by numerical evaluations.

Submitted to the Q. J. R. Meteorol. Soc. in August 2012. Accepted in April 2013. Early view on the QJRMS site http://onlinelibrary.wiley.com/doi/10.1002/qj.2182/abstract. 24 pages, 10 color figures. V2: add the arXiv links of Marquet (2011), Geleyn and Marquet (2012) and Marquet and Geleyn (2013)

References in corpus (3)

• Definition of a moist-air entropy potential temperature. Application to FIRE-I data flights
• On a general definition of the squared Brunt-Väisälä Frequency associated with the specific moist entropy potential temperature
• Moist-entropic vertical adiabatic lapse rates: the standard cases and some lead towards inhomogeneous conditions

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• Reply to the Comments of Olivier Pauluis to the paper "A Third-Law Isentropic Analysis of a Simulated Hurricane"
• Towards the use of conservative thermodynamic variables in data assimilation: a case study using ground-based microwave radiometer measurements
• Application of the second law to the atmosphere: impacts of the third-law definition for the moist-air entropy