Potential vorticity: Measuring consistency between GCM dynamical cores and tracer advection schemes

A numerically converged solution to the inviscid global shallow water equations on a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics, the other a finite-volume scheme on a cubed-sphere grid. Flow fields and various integral norms are both documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.

∥ q ∥_{\infty} = constant

for the true inviscid solution, even without the explicit calculation of such a solution.…”

Section: Inviscid Solutionmentioning

confidence: 99%

A test case for the inviscid shallow‐water equations on the sphere

Scott

Harris

Polvani

2015

“…Sources of systematic forecast error include inconsistencies in the dynamical core, insufficient resolution and errors due to the parametrizations of diabatic processes. As an example of dynamical core error, Whitehead et al () demonstrate inconsistency between model dynamical cores and tracer advection schemes in idealised breaking baroclinic wave simulations. Tracer advection schemes are required to passively advect the many tracers required in models, particularly chemical tracers in climate models, and hence such inconsistencies can lead to systematic errors.…”

Section: Introductionmentioning

confidence: 99%

A route to systematic error in forecasts of Rossby waves

Martínez‐Alvarado

Madonna

Gray

et al. 2015

Recent work has shown that both the amplitude of upper‐level Rossby waves and the tropopause sharpness decrease with forecast lead time for several days in some operational weather forecast systems. In this contribution, the evolution of error growth in a case‐study of this forecast error type is diagnosed through analysis of operational forecasts and hindcast simulations. Potential vorticity (PV) on the 320 K isentropic surface is used to diagnose Rossby waves. The Rossby‐wave forecast error in the operational ECMWF high‐resolution forecast is shown to be associated with errors in the forecast of a warm conveyor belt (WCB) through trajectory analysis and an error metric for WCB outflows. The WCB forecast error is characterised by an overestimation of WCB amplitude, a location of the WCB outflow regions that is too far to the southeast, and a resulting underestimation of the magnitude of the negative PV anomaly in the outflow. Essentially the same forecast error development also occurred in all members of the ECMWF Ensemble Prediction System and the Met Office MOGREPS‐15, suggesting that in this case model error made an important contribution to the development of forecast error in addition to initial condition error. Exploiting this forecast error robustness, a comparison was performed between the realised flow evolution, proxied by a sequence of short‐range simulations, and a contemporaneous forecast. Both the proxy to the realised flow and the contemporaneous forecast were produced with the Met Office Unified Model enhanced with tracers of diabatic processes modifying potential temperature and PV. Clear differences between proxy and forecast were found in the way potential temperature and PV are modified in the WCB. These results demonstrate that differences in potential temperature and PV modification in the WCB can be responsible for forecast errors in Rossby waves.

“…Previous studies of frontal formation have shown that the appearance of such large values of Q near surface fronts is to be expected (e.g. Whitehead et al ). In quasi‐geostrophic theory, the effect of surface variations in θ can be interpreted in terms of a surface δ ‐function contribution to the potential vorticity (Bretherton, ).…”

Section: Resultsmentioning

confidence: 99%

“…In a similar way, potential vorticity is a derived quantity in most atmospheric models. Whitehead et al () proposed an analogous test in which the evolution of potential vorticity is compared with the evolution of a tracer initialized to have the same distribution. Johnson et al , (; ) and Whitehead et al () discuss the advantages of such consistency.…”

Section: Lagrangian Diagnosticsmentioning

confidence: 99%

“…Here we combine this trajectory idea with the passive tracer idea of Johnson et al , (; ) and Whitehead et al () by making a three‐way comparison between directly predicted or derived model dynamical fields interpolated to the air parcel location, passive tracers interpolated to the air parcel location, and air parcel trajectory labels. …”

Section: Lagrangian Diagnosticsmentioning

confidence: 99%

See 1 more Smart Citation

A Lagrangian vertical coordinate version of the ENDGame dynamical core. Part II: Evaluation of Lagrangian conservation properties

Kavčič

Thuburn

2018

A baroclinic instability test case is used to compare the Lagrangian conservation properties of three versions of a semi‐implicit semi‐Lagrangian dynamical core: one using a height‐based vertical coordinate and two using a Lagrangian vertical coordinate. The Lagrangian coordinate versions differ in the choice of target levels to which model levels are reset after each step—the first uses the initial model level heights while the second uses quasi‐Lagrangian target levels. A range of diagnostics related to Lagrangian conservation are computed, including global entropy, unavailable energy, cross‐isentrope mass flux, and consistency of potential temperature and potential vorticity with passive tracers and parcel trajectories. The global entropy, unavailable energy, and cross‐isentrope fluxes do not suggest any clear advantage or disadvantage from the use of a Lagrangian vertical coordinate, though the cross‐isentrope flux reveals a flaw in the formulation of the remapping of potential temperature in the Lagrangian coordinate model at the top boundary. The use of a Lagrangian vertical coordinate with quasi‐Lagrangian target levels improves the consistency among potential temperature as a dynamical variable, potential temperature as a tracer and potential temperature on Lagrangian particle trajectories. It also improves consistency between a potential vorticity tracer and potential vorticity on Lagrangian particle trajectories. However, it degrades the consistency between model and tracer potential vorticity, as well as between model potential vorticity and potential vorticity on Lagrangian trajectories. This degradation appears to be related to the slopes of model levels, which are greater in the version with quasi‐Lagrangian target levels.