A baroclinic instability test case for atmospheric model dynamical cores

A deterministic initial-value test case for dry dynamical cores of atmospheric general-circulation models is presented that assesses the evolution of an idealized baroclinic wave in the northern hemisphere. The initial zonal state is quasi-realistic and completely defined by analytic expressions which are a steady-state solution of the adiabatic inviscid primitive equations with pressure-based vertical coordinates. A two-component test strategy first evaluates the ability of the discrete approximations to maintain the steady-state solution. Then an overlaid perturbation is introduced which triggers the growth of a baroclinic disturbance over the course of several days. The test is applied to four very different dynamical cores at varying horizontal and vertical resolutions. In particular, the NASA/NCAR Finite Volume dynamics package, the National Center for Atmospheric Research spectral transform Eulerian and the semi-Lagrangian dynamical cores of the Community Atmosphere Model CAM3 are evaluated. In addition, the icosahedral finite-difference model GME of the German Weather Service is tested. These hydrostatic dynamical cores represent a broad range of numerical approaches and, at very high resolutions, provide independent reference solutions. The paper discusses the convergence-with-resolution characteristics of the schemes and evaluates the uncertainty of the high-resolution reference solutions.