Articles | Volume 7, issue 1
Geosci. Model Dev., 7, 105–145, 2014

Special issue: Isaac Newton Institute programme on multiscale numerics for...

Geosci. Model Dev., 7, 105–145, 2014

Methods for assessment of models 14 Jan 2014

Methods for assessment of models | 14 Jan 2014

A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

P. H. Lauritzen1, P. A. Ullrich11, C. Jablonowski2, P. A. Bosler2, D. Calhoun3, A. J. Conley1, T. Enomoto4, L. Dong5, S. Dubey6, O. Guba7, A. B. Hansen14, E. Kaas8, J. Kent2, J.-F. Lamarque1, M. J. Prather9, D. Reinert10, V. V. Shashkin12,13, W. C. Skamarock1, B. Sørensen9, M. A. Taylor7, and M. A. Tolstykh12,13 P. H. Lauritzen et al.
  • 1National Center for Atmospheric Research, Boulder, Colorado, USA
  • 2University of Michigan, Department of Atmospheric, Oceanic and Space Sciences, Ann Arbor, Michigan, USA
  • 3Boise State University, Boise, Idaho, USA
  • 4Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, Japan
  • 5State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
  • 6Laboratoire de Météorologie Dynamique, Paris, France
  • 7Sandia National Laboratories, Albuquerque, New Mexico, USA
  • 8Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
  • 9Earth System Science Department, University of California, Irvine, California, USA
  • 10Deutscher Wetterdienst, Offenbach, Germany
  • 11University of California at Davis, Davis, California, USA
  • 12Institute of Numerical Mathematics, RAS, Moscow, Russia
  • 13Hydrometcentre of Russia, Moscow, Russia
  • 14National Institute of Water and Atmospheric Research, Lauder, New Zealand

Abstract. Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude–longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate–chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent.

The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data sets are made available to facilitate the process of model evaluation and scheme intercomparison.