A baroclinic instability test case for atmospheric model dynamical cores

Abstract

SUMMARY 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.

A mass‐conservative version of the semi‐implicit semi‐Lagrangian HIRLAM

“…The Jablonowski-Williamson baroclinic wave test case consists of an analytic steady-state zonal solution to the global primitive equations (Jablonowski and Williamson, 2006; hereafter referred to as JW06). The steady-state surface pressure is constant at 1000 hPa.…”

“…The new dynamical core has been validated using a recently developed idealized baroclinic wave test case for global dynamical cores (Jablonowski and Williamson, 2006). Except for a slight smoothing of a low-resolution run, the new model version was found to be accurate compared to a high-resolution global reference simulation when the artifacts introduced at the limited-area boundaries were, at least to first order, removed from the flow.…”

Scientific Final Report: COLLABORATIVE RESEARCH: CONTINUOUS DYNAMIC GRID ADAPTATION IN A GLOBAL ATMOSPHERIC MODEL: APPLICATION AND REFINEMENT

“…There is nothing intrinsic to EULAG that requires this. In the interest of employing more realistic geostrophically balanced states, we developed the anelastic nonhydrostatic variant of the test put forward in Jablonowski & Williamson (2006) that evinces baroclinic instability of mid-latitude jets. The crux of our development is to refine the geostrophically balanced ambient state of Jablonowski & Williamson, such that it forms the compatibility condition of EULAG; i.e., it satisfies the analytic model equations at the discretization level.…”

A scalable high-order discontinuous Galerkin method for global atmospheric modeling*

“…The baroclinic instability test proposed by Jablonowski and Williamson [6,7] is used to assess the evolution of an idealized baroclinic wave in the Northern Hemisphere. The baroclinic waves are triggered when overlaying the steady-state initial conditions with the zonal wind perturbation where as the initial conditions are given as quasi-realistic analytic expressions in [6,7].…”

“…The baroclinic waves are triggered when overlaying the steady-state initial conditions with the zonal wind perturbation where as the initial conditions are given as quasi-realistic analytic expressions in [6,7]. Numerical computations are performed for the conservative 3-D DG model with 9 th order polynomials (i.e., N v = N p = 10), horizontal resolution of 26 Lagrangian surfaces (i.e., N lev = 26 where N lev denotes the number of vertical levels) and total number of elements N elem = 216.…”