Simple algorithms to compute meridional overturning andbarotropic streamfunction on unstructured meshes

Abstract. Computation of barotropic and meridional overturning streamfunctions for models formulated on unstructured meshes is commonly preceded by interpolation to a regular mesh. This operation destroys the original conservation which can be then artificially imposed to make the computation possible. An elementary method is proposed that avoids interpolation and preserves conservation in a strict model sense. The method is described as applied to the discretization of the Finite volumE Sea ice -- Ocean Model (FESOM2) on triangular meshes. It however is generalizable to collocated vertex based discretization on triangular meshes and to both triangular and hexagonal C-grid discretizations.