  A model of the three-dimensional rotating compressible Euler equations on the
cubed sphere is presented. The model uses a mixed mimetic spectral element
discretization which allows for the exact exchanges of kinetic, internal and
potential energy via the compatibility properties of the chosen function
spaces. A Strang carryover dimensional splitting procedure is used, with the
horizontal dynamics solved explicitly and the vertical dynamics solved
implicitly so as to avoid the CFL restriction of the vertical sound waves. The
function spaces used to represent the horizontal dynamics are discontinuous
across vertical element boundaries, such that each horizontal layer is solved
independently so as to avoid the need to invert a global 3D mass matrix, while
the function spaces used to represent the vertical dynamics are similarly
discontinuous across horizontal element boundaries, allowing for the serial
solution of the vertical dynamics independently for each horizontal element.
The model is validated against standard test cases for baroclinic instability
within an otherwise hydrostatically and geostrophically balanced atmosphere,
and a non-hydrostatic gravity wave as driven by a temperature perturbation.
