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

Ofer Shamir, Nathan Paldor*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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 L2 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.

Original languageEnglish
Pages (from-to)2705-2714
Number of pages10
JournalQuarterly Journal of the Royal Meteorological Society
Volume142
Issue number700
DOIs
StatePublished - 1 Oct 2016

Bibliographical note

Publisher Copyright:
© 2016 Royal Meteorological Society

Keywords

  • inertia–gravity waves
  • planetary waves
  • Rossby waves
  • Rossby–Haurwitz

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