This paper introduces two methods for dynamically prescribing eddy-induced diffusivity, advection, and viscosity appropriate for primitive equation models with resolutions permitting the forward potential enstrophy cascade of quasi-geostrophic dynamics, such as operational ocean models and high-resolution climate models with km horizontal resolution and finer. Where quasi-geostrophic dynamics fail (e.g., the equator, boundary layers, and deep convection), the method reverts to scalings based on a matched two-dimensional enstrophy cascade. A principle advantage is that these subgrid models are scale-aware, meaning that the model is suitable over a range of grid resolutions: from mesoscale grids that just permit baroclinic instabilities to grids below the submesoscale where ageostrophic effects dominate. Two approaches are presented here using Large Eddy Simulation (LES) techniques adapted for three-dimensional rotating, stratified turbulence. The simpler approach has one nondimensional parameter, Λ, which has an optimal value near 1. The second approach dynamically optimizes Λ during simulation using a test filter. The new methods are tested in an idealized scenario by varying the grid resolution, and their use improves the spectra of potential enstrophy and energy in comparison to extant schemes. The new methods keep the gridscale Reynolds and Péclet numbers near 1 throughout the domain, which confers robust numerical stability and minimal spurious diapycnal mixing. Although there are no explicit parameters in the dynamic approach, there is strong sensitivity to the choice of test filter. Designing test filters for heterogeneous ocean turbulence adds cost and uncertainty, and we find the dynamic method does not noticeably improve over setting Λ = 1.

We describe a new way to apply a spatial filter to gridded data from models or observations, focusing on low‐pass filters. The new method is analogous to smoothing via diffusion, and its implementation requires only a discrete Laplacian operator appropriate to the data. The new method can approximate arbitrary filter shapes, including Gaussian filters, and can be extended to spatially varying and anisotropic filters. The new diffusion‐based smoother's properties are illustrated with examples from ocean model data and ocean observational products. An open‐source Python package implementing this algorithm, called gcm‐filters, is currently under development.