The non‐conservation of potential vorticity by a dynamical core compared with the effects of parametrized physical processes

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 nonconservation 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.

Processes Maintaining Tropopause Sharpness in Numerical Models

“…The key results from this study are The vertical PV contrast across the tropopause reduces relative to analyses with forecast lead time consistent with a smoothing of the isentropic PV gradient (Gray et al, ). On the time scales of the forecasts, the advection scheme of the model gives an exponential decay of the tropopause PV contrast to a finite value with a time scale of 20–24 h. A key component of the PV budget is the dynamics‐tracer inconsistency which quantifies the difference between the evolution of PV in the dynamical core and the evolution of PV through tracer advection (Saffin et al, ). The locations of the maxima in dynamics‐tracer inconsistency are different when composited relative to the 2 PVU surface of the advection‐only PV tracer rather than PV indicating that dynamics‐tracer inconsistency is having a direct effect on mass transport across the tropopause causing the q = 2 and q adv =2 surfaces to separate. The dynamics‐tracer inconsistency shows net negative tendencies near the tropopause level indicating a net transfer of mass from the stratosphere to the troposphere.…”

“…A key component of the PV budget is the dynamics‐tracer inconsistency which quantifies the difference between the evolution of PV in the dynamical core and the evolution of PV through tracer advection (Saffin et al, ). The locations of the maxima in dynamics‐tracer inconsistency are different when composited relative to the 2 PVU surface of the advection‐only PV tracer rather than PV indicating that dynamics‐tracer inconsistency is having a direct effect on mass transport across the tropopause causing the q = 2 and q adv =2 surfaces to separate. The dynamics‐tracer inconsistency shows net negative tendencies near the tropopause level indicating a net transfer of mass from the stratosphere to the troposphere.…”

“…Negative PV tendencies are consistent with a downward diabatic transport of mass by dilution of PV substance (Haynes & McIntyre, ). This is consistent with the isentropic map of ϵ I shown in Saffin et al () (their Figure 2c) where net negative tendencies are seen in the troughs where q = 2 is displaced from q adv =2.…”

“…The difference between these two changes gives This difference is calculated at every time step and accumulated as an additional tracer ( ϵ I ) in the same way as the physics tracers (i.e., equation . Saffin et al () showed that ϵ I is an important component of a model PV budget which can be desirable to minimize (e.g., Whitehead et al, ); however, exact conservation of PV is not necessarily a desirable property of a dynamical core because the cascade to smaller scales will be blocked at the grid scale (Thuburn, ).…”

“…The residual is a result of advecting multiple PV tracers with an imperfect advection scheme as well as any missing terms when summing increments over a time step. The residual was shown to be more than an order of magnitude smaller than the dominant physics PV tracers by Saffin et al ().…”