Comparing Ocean Eddy Parameterization Schemes via One-shot Optimization

Ocean circulations models often do not explicitly resolve small scale eddies owing to constraints on resolution and computation power, and hence ocean eddy parameterization remains a central problem in numerical modeling of oceans on climatic time scales. Often a proposed parameterization may be tested via implementation in a numerical model, integrating the model forwards in time, and comparing the resulting statistics of the parameterized model against a high resolution eddying reference. Here we take a complementary approach, seeking parameters (such as eddy diffusivities) which yield the minimal mismatch between the parameterized and eddy-resolving model. Eddy parameterization in the quasi-geostrophic limit is considered, and parameter optimization is carried out, with the parameterization quality defined using data from an eddying quasi-geostrophic model. Several parameterization schemes are considered, including potential vorticity diffusion and the Gent-McWilliams scheme, with and without scalings based upon the eddy energy, and the relative performance of the schemes in optimal configurations is discussed.