Scale-aware deterministic and stochastic parametrizations of eddy-mean flow interaction

Laure Zanna,Piergianluca Porta Mana,James Anstey,Tomos David,Thomas Bolton

doi:10.1016/j.ocemod.2017.01.004

Laure Zanna, Piergianluca Porta Mana + Show 3 more

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https://doi.org/10.1016/j.ocemod.2017.01.004

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Abstract

The role of mesoscale eddies is crucial for the ocean circulation and its energy budget. The sub-grid scale eddy variability needs to be parametrized in ocean models, even at so-called eddy permitting resolutions. Porta Mana and Zanna (2014) propose an eddy parametrization based on a non-Newtonian stress which depends on the partially resolved scales and their variability. In the present study, we test two versions of the parametrization, one deterministic and one stochastic, at coarse and eddy-permitting resolutions in a double gyre quasi-geostrophic model. The parametrization leads to drastic improvements in the mean state and variability of the ocean state, namely in the jet rectification and the kinetic-energy spectra as a function of wavenumber and frequency for eddy permitting models. The parametrization also appears to have a stabilizing effect on the model, especially the stochastic version. The parametrization possesses attractive features for implementation in global models: very little computational cost, it is flow aware and uses the properties of the underlying flow. The deterministic coefficient is scale-aware, while the stochastic parameter is scale- and flow-aware with dependence on resolution, stratification and wind forcing.

Highlights

With scales of 10–100 km, are turbulent features in the ocean derived from barotropic and baroclinic instabilities, and are strongly influenced by wind forcing and stratification
Eddy-permitting models remain unsuccessful at resolving the full mesoscale eddy field (Gnanadesikan and Hallberg, 2000; Hallberg, 2013) and its interaction with the large scales, and might not be able to do so in the near feature (Fox-Kemper et al, 2014)
The aim of our paper is to introduce an eddy parametrization, derived for eddy-permitting models, that makes use of the resolved variability, mimics the behaviour of Reynolds stresses such as sharpening ocean jets, scales with resolution and the flow, and feeds back energy lost due to viscosity

Summary

Introduction

With scales of 10–100 km, are turbulent features in the ocean derived from barotropic and baroclinic instabilities, and are strongly influenced by wind forcing and stratification. The parametrization mimics the effects of baroclinic instability, converting available potential energy into kinetic energy, and acts on buoyancy and passive tracers, but neglects eddy Reynolds stresses and sub-grid scale fluctuations. The horizontal resolution of the most recent generation of global climate models has increased to a scale close to the Rossby radius of deformation. These models, often called eddy-permitting, are starting to successfully capture some of the mesoscale eddy behaviour, especially at low- and mid- latitudes. Parametrizing sub-grid eddies, especially in eddy-permitting models, remains an important topic of research, as the previous generation of parametrizations, derived for coarse-resolution models, might not be able to successfully mimic the effects of the unresolved scales on the large-scale flow

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