A note on ‘Toward a stochastic parameterization of ocean mesoscale eddies’

Ian Grooms,Laure Zanna

doi:10.1016/j.ocemod.2017.03.007

Ian Grooms, Laure Zanna

Open Access

https://doi.org/10.1016/j.ocemod.2017.03.007

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Abstract

Porta Mana and Zanna (2014) recently proposed a subgrid-scale parameterization for eddy-permitting quasigeostrophic models. In this model the large-scale fluid is represented as a non-Newtonian viscoelastic medium, with a subgrid-stress closure that involves the Lagrangian derivative of large-scale quantities. This note derives this parameterization, including the nondimensional proportionality coefficient, using only two statistical assumptions: that the subgrid-scale term is locally homogeneous and decorrelates rapidly in space. The parameterization is then verified by comparing against eddy-resolving quasigeostrophic simulations, independently reproducing the results of Porta Mana and Zanna in a simpler model.

Highlights

Continuing improvement in the spatial resolution of operational global ocean models has led to recent interest in subgrid-scale parameterizations appropriate to models that partially resolve mesoscale eddy dynamics
They performed thorough multiscale statistical analysis of an eddy-resolving quasigeostrophic (QG) gyre simulation, similar to the ‘dynamically consistent’ diagnostic framework from Berloff (2005a), studying in particular the component of the time tendency of the large-scale potential vorticity (PV) that is induced by subgrid-scale terms
We have provided an a priori derivation of the parameterization proposed by Porta Mana and Zanna (2014) using only two statistical assumptions on the eddy source term S ∗: that its variance changes minimally from one coarse grid point to the, and that its value at one coarse grid point is approximately uncorrelated with its value at neighboring grid points

Summary

Introduction

Continuing improvement in the spatial resolution of operational global ocean models has led to recent interest in subgrid-scale parameterizations appropriate to models that partially resolve mesoscale eddy dynamics. Fox-Kemper and Menemenlis (2008) advocate a nonlinear viscosity based on Leith’s (Leith, 1996) adaptation to quasi-2D dynamics of Smagorinsky’s (Smagorinsky, 1963) successful large eddy simulation (LES) approach. Preprint submitted to Ocean Modelling those above They performed thorough multiscale statistical analysis of an eddy-resolving quasigeostrophic (QG) gyre simulation, similar to the ‘dynamically consistent’ diagnostic framework from Berloff (2005a), studying in particular the component of the time tendency of the large-scale potential vorticity (PV) that is induced by subgrid-scale terms. This parameterization relates the subgrid-scale term to the Lagrangian time derivative of the large-scale potential vorticity They showed that an analogy between the parameterization, which includes a time-tendency of largescale quantities, and the theory of non-Newtonian fluids of second grade or ‘Rivlin-Ericksen fluids’ (Rivlin and Ericksen, 1997; Dunn and Fosdick, 1974; Truesdell and Rajagopal, 2010) can be drawn. March 8, 2017 geneity and rapid spatial decorrelation of the subgridscale term

Theoretical Development

Experimental Configuration & Results

Conclusions