The Matsuno baroclinic wave test case

Abstract

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.

On the role of domain aspect ratio in the westward intensification of wind-driven surface ocean circulation

“…reader should refer to Gildor et al (2016) and Shamir et al (2019) for a more detailed description of the solver. The reader should also note that dimensional variables mentioned in this section are accompanied by an asterisk ( * ).…”

Analysis of mimetic finite volume schemes on classical and moist shallow water models considering topography based local refinement in spherical Voronoi grids

“…We evaluate the behavior of TRSK on the grid with local refinement on the Andes applying standard shallow water test cases proposed in the literature (Galewsky et al, 2004;Williamson et al, 1992) and also the test case recently proposed by Shamir et al (2019).…”

“…We will the grid generator and shallow water model developed by Peixoto (2013) called iModel. We developed in iModel the capabilities of topography based local refinement, convective shallow water model and the test case proposed by Shamir et al (2019).…”

“…We will make small changes on these tests since our grids are refined in South Hemisphere and we wish to investigate the impact of the refined region. Recently, a new test has been proposed by Shamir et al (2019) and this test will also be included in our tests. Summarizing, our test set consist of: 5.…”

“…The instability of Rossby-Haurwitz is undesirable since we cannot run this test for more than 20 days, because after that the wave loses the shape. A new test case has been recently proposed by Shamir et al (2019), which is known as Matsuno baroclinic wave test case. In contrast with the Rossby-Haurwitz test case that uses analytical solutions of the nonlinear barotropic vorticity equation as initial conditions, this test case uses as initial conditions the analytic solution for the shallow water equations linearised on beta plane obtained by Matsuno (1966).…”