Spherical shallow-water wave simulation by a cubed-sphere finite-difference solver

We consider the test suite for the shallow-water (SW) equations on the sphere suggested by Paldor in earlier work. This series of tests consists of zonally propagating wave solutions on the full sphere. Two series of solutions are considered. The first series is referred to as "barotropic". It consists of an extension of the Rossby-Haurwitz test case. The second series, referred to as "baroclinic", consists of a generalisation of the Matsuno solution to the linearized SW equations in an equatorial channel. The Hermitian Compact Cubed Sphere (HCCS) model which is used in this paper is a recently introduced SW solver on the sphere. The spatial approximation is a centred finite-difference scheme based on high-order differencing along great circles. The time stepping is performed by the explicit RK4 scheme or by an exponential scheme. For both barotropic and baroclinic test case series, the results show a very good agreement of the numerical solution with the analytic one, even for long time simulations.