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ABSTRACT
The authors propose a parameterization for restratification by mixed layer eddies that develop from baroclinic instabilities of ocean fronts. The parameterization is cast as an overturning streamfunction that is proportional to the product of horizontal buoyancy gradient, mixed layer depth, and inertial period. The parameterization has remarkable skill for an extremely wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. In this paper a coarse resolution prognostic model of the parameterization is compared with submesoscale mixed layer eddy resolving simulations. The parameterization proves accurate in predicting changes to the buoyancy. The climate implications of the proposed parameterization are estimated by applying the restratification scaling to observations: the mixed layer depth is estimated from climatology, and the buoyancy gradients are from satellite altimetry. The vertical fluxes are comparable to monthly mean air-sea fluxes in large areas of the ocean and suggest that restratification by mixed layer eddies is a leading order process in the upper ocean. Critical regions for ocean-atmosphere interaction, such as deep, intermediate, and mode water formation sites, are particularly affected.
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1. Introduction
Boccaletti et al. (2007, hereafter BFF) and FoxKemper et al. (2008a, hereafter FFH) study the restratification due to ageostrophic baroclinic instabilities that develop at fronts in the ocean surface mixed layer. BFF and FFH study the restratification once the instabilities have reached finite amplitude, by focusing on a mixed layer (ML) front in a reentrant channel. First, the front geostrophically adjusts (Tandon and Garrett 1995) and then yields to ageostrophic baroclinic instabilities (Stone 1972a). FFH propose that the primary effect of these instabilities on the mean flow is to overturn the front, converting horizontal density gradients to vertical gradients.
The baroclinic instabilities that lead to finite-amplitude mixed layer eddies (MLEs) occur on length scales near the deformation radius of the ML, which is 0(1 km) because of the weak stratification in the ML. General circulation models (GCMs) used for climate studies do not resolve these small scales, so the overturning effect of MLEs must be parameterized. Even "eddy resolving" GCMs with O(10 km) grids require parameterization of the still unresolved submesoscale. The buoyancy fluxes needed for the buoyancy budget in a GCM may be spectrally decomposed into three categories: fluxes...