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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Discussion papers | Copyright
https://doi.org/10.5194/gmd-2018-260
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Methods for assessment of models 05 Nov 2018

Methods for assessment of models | 05 Nov 2018

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This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).

The Matsuno baroclinic wave test case

Ofer Shamir, Itamar Yacoby, and Nathan Paldor Ofer Shamir et al.
  • Fredy and Nadine Herrmann Institute of Earth Sciences, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, Israel

Abstract. The analytic wave-solutions obtained by Matsuno (1966) in his seminal work on equatorial waves provide a simple and informative way of assessing atmospheric and oceanic models by measuring the accuracy with which they simulate these waves. These solutions approximate the solutions of the shallow water equations on the sphere for small speeds of gravity waves such as those of the baroclinic modes in the atmosphere and ocean. This is in contrast to the solutions of the non-divergent barotropic vorticity equation, used in the Rossby-Haurwitz test case, which are only accurate for large speeds of gravity waves such as those of the barotropic mode. The proposed test case assigns specific values to the wave-parameters (gravity wave speed, zonal wave-number, meridional wave-mode and amplitude) for both planetary and inertia gravity waves, and confirms the accuracy of the simulation by employing Hovmöller diagrams and temporal and spatial spectra. The proposed test case is successfully applied to a standard finite-difference, equatorial, non-linear, shallow water model in spherical coordinates, which demonstrates that Matsuno’s wave-solutions can be accurately simulated for at least 10 wave-periods, which for oceanic planetary waves is nearly 1300 days. In order to facilitate the use of the proposed test case, we provide Matlab, Python and Fortran codes for computing the analytic solutions at any time on arbitrary latitude-longitude grids.

Ofer Shamir et al.
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Latest update: 13 Nov 2018
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Short summary
The development of atmospheric and oceanic models in spherical coordinates requires a quantitative assessment of the accuracy of the models’ simulations. A tool for such quantitative assessment is proposed based on analytic wave solutions of the linearized governing equations. New error measures are employed which are more relevant then formerly employed error measures for the single-mode simulations used in the proposed test case. Codes are supplied for calculating the required initial fields.
The development of atmospheric and oceanic models in spherical coordinates requires a...
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