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Due to the massive disparity between the largest and smallest eddies in theatmosphere and ocean, it is not possible to simulate these flows byexplicitly resolving all scales on a computational grid. Instead the largescales are explicitly resolved, and the interactions between the unresolvedsubgrid turbulence and large resolved scales are parameterised. If theseinteractions are not properly represented then an increase in resolution willnot necessarily improve the accuracy of the large scales. This has been asignificant and long-standing problem since the earliest climate simulations.Historically subgrid models for the atmosphere and ocean have been developedin isolation, with the structure of each motivated by different physicalphenomena. Here we solve the turbulence closure problem by determining theparameterisation coefficients (eddy viscosities) from the subgrid statisticsof high-resolution quasi-geostrophic atmospheric and oceanic simulations.These subgrid coefficients are characterised into a set of simple unifyingscaling laws, for truncations made within the enstrophy-cascading inertial range. The ocean additionally has an inverse energy cascading range, withinwhich the subgrid model coefficients have different scaling properties.Simulations adopting these scaling laws are shown to reproduce the statisticsof the reference benchmark simulations across resolved scales, with orders ofmagnitude improvement in computational efficiency. This reduction in bothresolution dependence and computational effort will improve the efficiencyand accuracy of geophysical research and operational activities that requiredata generated by general circulation models, including weather, seasonal,and climate prediction; transport studies; and understanding naturalvariability and extreme events

Theoretical comparison of subgrid turbulence in atmospheric and oceanic quasi-geostrophic models