Horizontal fluxes of heat and other scalar quantities in the ocean are due to correlations between the horizontal velocity and tracer fields. However, the limited spatial resolution of ocean models means that these correlations are not fully resolved using the velocity and temperature evaluated on the model grid, due to the limited spatial resolution and the boxcar-averaged nature of the velocity and the scalar field. In this article, a method of estimating the horizontal flux due to unresolved spatial correlations is proposed, based on the depth-integrated horizontal transport from the seafloor to the density surface whose spatially averaged height is the height of the calculation. This depth-integrated horizontal transport takes into account the subgrid velocity and density variations to compensate the standard estimate of horizontal transport based on staircase-like velocity and density. It is not a parameterization of unresolved eddies, since it utilizes data available in ocean models without relying on any presumed parameter such as diffusivity. The method is termed the horizontal residual mean (HRM). The method is capable of estimating the spatial-correlation-induced water transport in a 1/4° global ocean model, using model data smoothed to 3/4°. The HRM extra overturning has a peak in the Southern Ocean of about 1.5 Sv (1 Sv ≡ 106 m3 s−1). This indicates an extra heat transport of 0.015 PW on average in the same area. It is expected that implementing the scheme in a coarse-resolution ocean model will improve its representation of lateral heat fluxes.

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