Assessment of mesoscale eddy parameterizations for a single‐basin coarse‐resolution ocean model

Abstract

In this study we explore the ability of three parameterization schemes to represent mesoscale eddies' effects in a single, idealized ocean basin. We first carry out an eddy‐resolving simulation with an ocean general circulation model (GCM). The three schemes tested are the traditional Fickian diffusion and the Green‐Stone (GS) and Gent‐McWilliams (GM) parameterizations. Evaluation of the divergence of the eddy heat flux from the reference simulation in the time‐averaged thermal balance shows that eddies contribute significantly to the balance only in a geographically limited area adjacent to the western boundary around the separation point of the midlatitude jet. For this region, diagnostic tests are carried out comparing the local properties of the eddy heat flux evaluated from the fine‐resolution eddy‐resolving reference simulation with the parameterized fluxes diagnosed according to the three schemes. Evaluation of the Fickian diffusion shows that the components of the eddy heat flux are not down the temperature gradient in about half of the domain. The GS parameterization is assessed by examining the relative orientation of the isopycnal surface and the eddy heat flux vector. The relative orientation falls outside the range implicitly assumed by the GS parameterization in about half of the domain. Similarly, the GM scheme simulates the wrong sign for the divergence of the eddy heat flux in about half of the domain. Comparison of the divergences predicted with the schemes in the most energetic subdomain of the western region shows that all of them have some skill but does not identify any one scheme as being superior to the others, and two of them, GS and GM, fail in the western boundary current by predicting the wrong sign of the divergence. The incorrect orientation of the eddy heat flux vector in the test of the GS scheme implies that mean flow kinetic energy is an important source of eddy energy, and this is a likely reason why the GS and GM schemes do not do better. We carry out a further assessment of the parameterization schemes by implementing them in an ocean GCM in coarse‐resolution experiments, thus mimicking the actual procedure used in climate simulations. All the parameterization schemes can be tuned to reproduce with some accuracy some of the climatological diagnostic quantities, hence their relative success in climatological coarse‐resolution simulations. However, once again, no one scheme is noticeably better than the others. We note that our results only apply to parameterizations of eddies generated in western boundary currents and their extensions.