Abstract
Numerical models of the atmosphere combine a dynamical core, which approximates solutions to the adiabatic, frictionless governing equations for fluid dynamics, with tendencies arising from the parametrization of other physical processes. Since potential vorticity (PV) is conserved following fluid flow in adiabatic, frictionless circumstances, it is possible to isolate the effects of non‐conservative processes by accumulating PV changes in an air‐mass‐relative framework. This ‘PV tracer technique’ is used to accumulate separately the effects on PV of each of the different non‐conservative processes represented in a numerical model of the atmosphere. Dynamical cores are not exactly conservative because they introduce, explicitly or implicitly, some level of dissipation and adjustment of prognostic model variables which acts to modify PV. Here, the PV tracers technique is extended to diagnose the cumulative effect of the non‐conservation of PV by a dynamical core and its characteristics relative to the PV modification by parametrized physical processes.Quantification using the Met Office Unified Model reveals that the magnitude of the non‐conservation of PV by the dynamical core is comparable to those from physical processes. Moreover, the residual of the PV budget, when tracing the effects of the dynamical core and physical processes, is at least an order of magnitude smaller than the PV tracers associated with the most active physical processes. The implication of this work is that the non‐conservation of PV by a dynamical core can be assessed in case‐studies with a full suite of physics parametrizations and directly compared with the PV modification by parametrized physical processes. The non‐conservation of PV by the dynamical core is shown to move the position of the extratropical tropopause while the parametrized physical processes have a lesser effect at the tropopause level.
Highlights
Potential vorticity (PV) thinking has become a key concept in dynamical meteorology
We show that this ‘dynamics-tracer inconsistency’ is comparable to the effects on PV of parametrized physical processes for a case-study with the Met Office’s Unified Model (MetUM) and that the majority of the ‘dynamics-tracer inconsistency’ in the MetUM can be attributed to non-conservation of PV by the dynamical core
By considering the evolution of the PV budget across a time step, we show that ε is completely accounted for by three terms: ‘dynamics-tracer inconsistency’ to be defined below based on the inconsistency investigated by Whitehead et al (2015); ‘missing PV’ which accounts for any increments in PV not attributed to a dynamical or physical process; and a ‘splitting error’ which accounts for the difference between numerical diffusion acting on multiple tracers of PV and the numerical diffusion acting on a single field representing the sum of those PV tracers
Summary
Potential vorticity (PV) thinking has become a key concept in dynamical meteorology. PV has two key properties, conservation (Ertel, 1942) and invertibility as discussed in Hoskins et al (1985). Invertibility means that the PV distribution, with appropriate boundary conditions, is sufficient to diagnose all of the dry dynamical variables to the approximation of a given balance condition. The usefulness of PV thinking depends on the accuracy of the balanced dynamics. Davis et al (1996) demonstrated that most of the dynamics of an intense extratropical cyclone could be quantified using the balance equations of Charney (1955). McIntyre and Norton (2000) showed that higher-order PV-based balanced models were capable of producing simulations ‘remarkably similar’ to the full unbalanced equations for shallow-water simulations The usefulness of PV thinking depends on the accuracy of the balanced dynamics. Davis et al (1996) demonstrated that most of the dynamics of an intense extratropical cyclone could be quantified using the balance equations of Charney (1955). McIntyre and Norton (2000) showed that higher-order PV-based balanced models were capable of producing simulations ‘remarkably similar’ to the full unbalanced equations for shallow-water simulations
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