On the use of potential vorticity tendency equations for diagnosing atmospheric dynamics in numerical models

This study critically assesses potential vorticity (PV) tendency equations used for analysing atmospheric convective systems. A generic PV tendency format is presented to provide a framework for comparing PV tendency equations, which isolates the contributions to PV tendency from wind and mass field changes. These changes are separated into forcing terms (e.g., diabatic or friction) and flow adjustment and evolution terms (i.e., adiabatic motions). One PV tendency formulation analysed separates PV tendency into terms representing PV advection and diabatic and frictional PV sources. In this form the PV advection is shown to exhibit large cancellation with the diabatic forcing term when used to analyse deep convective systems, which compromises the dynamical insight the PV tendency analysis should provide. The isentropic PV substance tendency formulation of Haynes and McIntyre does not suffer from this cancellation problem. However, while the Haynes and McIntyre formulation may be appropriate for many convective system applications, there are likely to be some applications in which the formulation is difficult to apply or is not ideal. This study introduces a family of PV tendency equations in geometric coordinates that is free from the deficiencies of the above formulations. Simpler forms are complemented by more complex forms that expand the vorticity tendency term to offer additional insight into flow dynamics. The more complex forms offer similar insight to the influential Haynes and McIntyre isentropic formulation.