Semi-Lagrangian advection on conformal-cubic grids

It has been demonstrated by McGregor that semi-lagrangian advection techniques may be efficiently applied to a cubic gnomonic grid on the sphere. Despite the nonorthogonal nature of that grid, the accuracy is superior to that of conventional latitude-longitude grids. The present paper demonstrates even greater accuracy by applying similar techniques to the related conformal-cubic grid devised by Rancic et al.; an important new feature is a simple iterative technique for the inverse calculation of grid coordinates. Advection over the vertices of the grid exhibits none of the problems that occur over the poles of a latitude-longitude grid. A stretched grid configuration is also presented showing further improvements. It is finally shown that the departure points may be interpolated onto a B-grid version and advection performed simply on the staggered grid without loss of accuracy.