Ertel’s potential vorticity (PV) is an important quantity in atmospheric
dynamics that succinctly encompasses the principles of mass, momentum,
and energy conservation and is applicable to all scales of motion. In
this paper, we describe the implementation of a PV diagnostics package
into the atmospheric component of the Model for Prediction Across Scales
(MPAS), a fully compressible nonhydrostatic global model that enables
regional mesh refinement to convection-permitting resolutions and is
highly suited for studies on multiscale process interactions and
forecast error-growth dynamics.
The version of the PV diagnostics package emphasized herein will be
included in an upcoming MPAS release and significantly improves upon an
original version that was introduced in MPAS v5.0. Specifically, this
revised version enables the calculation of the full Eulerian PV budget
at each time step Δt (i.e., the instantaneous budget) and the
accumulation of PV tendencies throughout the model integration (i.e.,
the accumulated budget). Through the formulation of the discretized PV
budget equation and global simulations conducted on a 15–3-km
variable-resolution mesh, we demonstrate that the instantaneous PV
budget closes down to machine roundoff in both single- and
double-precisions. Further, we find that the PV budget computed using
accumulated PV tendencies leads to a small source of residual that
arises due to the inherent nonlinearity of PV, which leads to leads to
mathematical inconsistencies between the discretized equation for
calculating the PV budget over any arbitrary period longer than Δt and
that which results from accumulating the PV tendencies themselves over
successive time steps.