Application of the Synchronized B-Grid Staggering for Solution of the Shallow-Water Equations on the Spherical Icosahedral Grid

Abstract

Abstract A shallow-water model using the hexagonal synchronized B grid (SB grid) is developed on the spherical icosahedral grid. The SB grid adopts the same variable arrangement as the ZM grid, but does not suffer from a computational mode problem of the ZM grid since interactions in the extra degrees of freedom of velocity fields through the nonlinear terms are excluded. For better representations of the geostrophic balance, a quadratic reconstruction of fluid height inside hexagonal/pentagonal cells is used to configure the gradient with the second-order accuracy. When nongeostrophic motions are more dominant than geostrophic ones, smaller-scale noises arise. To prevent a decoupling of the velocity fields, a hyperviscosity is added to force velocities adjacent to each other to evolve synchronously. Some standard tests are performed to examine the SB-grid shallow-water model. The model is almost second-order accurate if both the initial conditions and the surface topography are smooth and if the influence of the hyperviscosity is small. The SB-grid model is superior to a C-grid model regarding the convergence of error norms in a steady-state geostrophically balanced flow test, while it is inferior to that concerning conservation of total energy in a case of flow over an isolated mountain. An advantage of the SB-grid model is that both accuracy and stability are weakly sensitive to whether a grid optimization is applied or not. The SB grid is an attractive alternative to the conventional A grid and is competitive with the C grid on the spherical icosahedral grid.