Second order potential vorticity and its potential applications

A new invariant, the second order potential vorticity （SPV）, is derived in this paper. SPV is the dot product of vorticity and the potential vorticity （PV） gradient, and is proven conservative for a compressible, adiabatic and frictionless atmosphere. Research shows that the new invariant may be used to indicate the evolution of PV, because SPV includes all the information that determines PV evolution： the wind field, and the PV gradient. Furthermore, SPV is capable of diagnosing heavy precipitation because of the strong signals it presents in areas of heavy rainfall. SPV also shows great potential as a comprehensive con served quantity for indicating the dynamical tropopause and baroclinic instability.