Mimetic Interpolation of Vector Fields on Arakawa C/D Grids

Interpolation methods for vector fields whose components are staggered on horizontal Arakawa C or D grids are presented. The interpolation methods extend bilinear and area-weighted interpolation, which are widely used in Earth sciences, to work with vector fields (essentially discretized versions of differential 1-forms and 2-forms). The interpolation methods, which conserve the total flux and enforce Stokes’ theorem to near-machine accuracy, are a natural complement to discrete exterior calculus and finite element exterior calculus discretization methods.