Abstract
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 colocated vertex-based discretization on triangular meshes and to both triangular and hexagonal C-grid discretizations.
Highlights
A considerable progress has been achieved in the development of global ocean circulation models working on horizontally unstructured meshes such as FESOM1.4 (Wang et al, 2014), MPAS-Ocean (Ringler et al, 2013), FESOM2 (Danilov et al, 2017) and ICON-Ocean (Korn, 2017)
Any interpolation on a regular mesh violates the sense in which continuity is satisfied in a model and introduces errors which, while often acceptable for computing local fluxes and transports, are very annoying in computations of global or basin streamfunctions where large positive and negative contributions are combined together
In the early version of FESOM, based on continuous finite elements, the situation was exacerbated by continuity being formulated in a weighted sense, without explicitly computed fluxes (Sidorenko et al, 2009)
Summary
A considerable progress has been achieved in the development of global ocean circulation models working on horizontally unstructured meshes such as FESOM1.4 (Wang et al, 2014), MPAS-Ocean (Ringler et al, 2013), FESOM2 (Danilov et al, 2017) and ICON-Ocean (Korn, 2017). By refining in dedicated areas of the world ocean, these models may resolve dynamics that would otherwise require nesting or using a higher resolution globally. Since these models still use vertically aligned meshes, the overhead of horizontally unstructured mesh is minimized because the horizontal neighborhood information is valid for the entire vertical column and becomes negligible as the number of vertical levels is increased. Any interpolation on a regular mesh violates the sense in which continuity is satisfied in a model and introduces errors which, while often acceptable for computing local fluxes and transports, are very annoying in computations of global or basin streamfunctions where large positive and negative contributions are combined together. In the early version of FESOM, based on continuous finite elements, the situation was exacerbated by continuity being formulated in a weighted sense, without explicitly computed fluxes (Sidorenko et al, 2009)
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