Resolution dependence of the tropopause inversion layer in an idealized modelling framework

Recent research has shown that profiles of static stability in the extratropical tropopause region have a pronounced and very sharp peak right above the tropopause. The underlying mechanisms for this so-called "Tropopause Inversion Layer" (short TIL) are not well understood, although there is some evidence that balanced dynamics plays a role. Numerical models typically feature some kind of TIL, but it is often much weaker than observed.

Here we investigate the TIL in an idealized purely dynamical framework with special focus on the dependence of TIL strength on numerical resolution. Axisymmetric upper tropospheric anticyclones are constructed by specifying potential vorticity (PV) and solving the nonlinear PV-inversion problem. The PV-distribution has a smooth but near discontinuous change of PV across the tropopause in a transition region of depth δ. Parameters of interest are the amplitude A of the tropopause anomaly and the transition depth δ. As it turns out, results from similar previous PV-inversion studies are problematic, because they were by no means numerically converged.

In a first step we study the convergence of the numerical solution for fixed δ. Special care is given to alloting horizontal versus vertical resolution. It turns out that the strength of the TIL increases with increasing resolution until the transition zone is resolved by about 30 grid points. In a second step we use the numerical solutions to study the behavior as δ. goes to zero. This limit can lead to very strong TIL's, but no indications were found for divergent behavior. We conclude that an uppper tropospheric anticyclone can be associated with a very strong TIL, and that the numerical resolution of typical global and mesoscale models is likely to underestimate the strength of the TIL owing to limited numerical resolution.