Two interpolation methods for vector fields that conserve fluxes and line integrals

Dr Alexander Pletzer1, Dr Wolfgang Hayek1, Dr Samantha  Adams2

1NeSI/NIWA, Hataitai, New Zealand, 2UK Met Office , Exeter, United Kingdom


Interpolation was invented by the old Babylonians in 2000-1700 BC but it is only since 1999 that conservative interpolation has been introduced and applied to earth sciences.  Due to the need to preserve the total amount of water, energy etc., conservative interpolation has become one of the most widely used regridding methods. We show that conservative interpolation is just one member of a larger family of so-called mimetic interpolation methods, which conserve volume, area and line integrals. Area/line conserving interpolation is applicable to vector fields with face/edge centred staggering, respectively. Using grids from the next generation weather and climate prediction code LFRic, we demonstrate the benefit of mimetic interpolation in the case of unstructured grids with arbitrary, quadrilateral cells. In addition to conserving vorticity and fluxes, mimetic methods are immune to pole-like singularities and can be extended to work with partially masked cells, which often arise in earth sciences.


Alex Pletzer is a physicist who drifted towards computational science and is now a research software engineer for New Zealand eScience Infrastructure (NeSI) at the National Institute of Water and Atmospheric research (NIWA).


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