An analytical solution for linear gravity and sound waves on the sphere as a test for compressible, non-hydrostatic numerical models

An analytical solution for the expansion of gravity and sound waves for the linearized form of the fully compressible, non-hydrostatic, shallow atmosphere Euler equations on the sphere is derived. The waves are generated by a weak initial temperature and density perturbation of an isothermal atmosphere. The derived analytical solution can be used as a benchmark to assess dynamical cores of global models based on the above-mentioned (in general nonlinear) equation system. Three different test configurations, with or without Coriolis force or additional advection, are discussed. Convergence studies of the newly developed ICOsahedral Non-hydrostatic global model (ICON) against this solution are performed.