The Geography of Numerical Mixing in a Suite of Global Ocean Models

R. M. Holmes*, J. D. Zika, S. M. Griffies, A. Mc C. Hogg, A. E. Kiss, M. H. England

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


Numerical mixing, defined here as the physically spurious tracer diffusion due to the numerical discretization of advection, is known to contribute to biases in ocean models. However, quantifying numerical mixing is nontrivial, with most studies utilizing targeted experiments in idealized settings. Here, we present a water mass transformation-based method for quantifying numerical mixing that can be applied to any conserved variable in general circulation models. Furthermore, the method can be applied within individual fluid columns to provide spatial information. We apply the method to a suite of global ocean model simulations with differing grid spacings and subgrid-scale parameterizations. In all configurations numerical mixing drives diathermal heat transport of comparable magnitude to that associated with explicit parameterizations. Numerical mixing is prominent in the tropical thermocline, where it is sensitive to the vertical diffusivity and resolution. At colder temperatures numerical mixing is sensitive to the presence of explicit neutral diffusion, suggesting that it may act as a proxy for neutral diffusion when it is explicitly absent. Comparison of otherwise equivalent 1/4° and 1/10° configurations with grid-scale dependent horizontal viscosity shows only a modest enhancement in numerical mixing at 1/4°. However, if the lateral viscosity is maintained while resolution is increased then numerical mixing is reduced by almost 35%. This result suggests that the common practice of reducing viscosity in order to maximize permitted variability must be considered carefully. Our results provide a detailed view of numerical mixing in ocean models and pave the way for improvements in parameter choices and numerical methods.

Original languageEnglish
Article numbere2020MS002333
JournalJournal of Advances in Modeling Earth Systems
Issue number7
Publication statusPublished - Jul 2021


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