Note about the "NE" variable. This is the name of a Fortran variable and also used in CIME XML files to refer to cubed sphere grids. It is meaningless jargon to most people. For written documents we recommend referring to grids by their resolution in km. For the quasi-uniform cubed-sphere grid, average grid spacing at the equator is a good measure of the resolutions.
For cubed sphere grids (CAM-SE Grid Overview ), NE is the number of spectral elements along each cube face. Thus the total number of elements N = 6 NE^2.
For regionally refined grids, internally in the code NE=0 and the number of elements N is read in from the Exodus RRM mesh file. RRM grids can be any quadrilateral tiling of the sphere and may not be based on cubed-sphere grids.
For any spectral element grid with N elements, the number of unique points (physics columns) is (np-1)^2 * N + 2, where each element contains a np x np tensor product of Gauss-Lobatto points.
...