  A new grid system on a sphere is proposed that allows for straight-forward
implementation of both spherical-harmonics-based spectral methods and
gridpoint-based multigrid methods. The latitudinal gridpoints in the new grid
are equidistant and spectral transforms in the latitudinal direction are
performed using Clenshaw-Curtis quadrature. The spectral transforms with this
new grid and quadrature are shown to be exact within the machine precision
provided that the grid truncation is such that there are at least 2N + 1
latitudinal gridpoints for the total truncation wavenumber of N. The new grid
and quadrature is implemented and tested on a shallow-water equations model and
the hydrostatic dry dynamical core of the global NWP model JMA-GSM. The
integration results obtained with the new quadrature are shown to be almost
identical to those obtained with the conventional Gaussian quadrature on
Gaussian grid. Only minor code changes are required to any Gaussian-based
spectral models to employ the proposed quadrature.
