Potential Vorticity: Measuring Consistency Between GCM Dynamical Cores and Tracer Advection Schemes

Ertel's potential vorticity (PV) is used as a diagnostic tool to give a direct comparison between the treatment of PV in the dynamics and the integration of PV as a passive tracer, yielding a systematic evaluation of a model's consistency between the dynamical core's integration of the equations of motion and its tracer transport algorithm. Several quantitative and qualitative metrics are considered to measure the consistency, including error norms and grid-independent probability density functions. Comparisons between the four dynamical cores of the National Center for Atmospheric Research's (NCAR) Community Atmosphere Model version 5.1 (CAM) are presented. We investigate the consistency of these dynamical cores in an idealized setting: the presence of a breaking baroclinic wave. For linear flow, before the wave breaks, the consistency for each model is good. As the flow becomes nonlinear, the consistency between dynamic PV and tracer PV breaks down, especially at small scales. Large values of dynamic PV are observed that do not appear in the tracer PV. The results indicate that the spectral-element (CAM-SE) dynamical core is the most consistent of the dynamical cores in CAM, however the consistency between dynamic PV and tracer PV is related to and sensitive to the diffusive properties of the dynamical cores.