A quantitative test case for global-scale dynamical cores based on analytic wave solutions of the shallow-water equations

作者：Shamir Ofer; Paldor Nathan^*

来源：Quarterly Journal of the Royal Meteorological Society, 2016, 142(700): 2705-2714.

DOI：10.1002/qj.2861

• Rossby-Haurwitz
• inertia-gravity waves
• Rossby waves
• planetary waves

Recently derived analytic wave solutions of the shallow-water equations (SWEs) on the rotating spherical Earth are employed to construct a test case for hydrostatic dynamical cores of global-scale general circulation models (GCMs). The proposed test case is more relevant to the SWEs than the frequently used Rossby Haurwitz test case which is based on wave solutions of the non-divergent barotropic vorticity equation and not the SWEs. The applicability of the proposed test case to operational GCMs is demonstrated by using the spectral Eulerian dynamical core of the atmospheric component of NCAR's Community Earth System Model to simulate the analytic solutions. An initial slowly propagating Rossby wave and a fast eastward propagating inertia gravity wave are both accurately simulated for 100 wave periods, in order to quantify the accuracy of the simulations, two error measures are suggested which complement the conservation of global energy and, unlike the frequently used L-2 error-measure, provide independent assessments of the errors in the phase speeds and the meridional structures of the simulated waves and are therefore more relevant to periodic wave solutions.

• 出版日期2016-10