Effects of heterogeneous surface boundary conditions on parameterized oceanic deep convection

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Abstract

Vertical mixing and deep convection are routinely parameterized in basin-scale and global ocean general circulation models. These parameterizations are designed to work with homogeneous surface boundary conditions for an individual grid cell. A partial ice cover, however, yields heterogeneous fluxes of buoyancy that are not resolved by the computational grid. The effects of such heterogeneous surface boundary conditions are explored by comparing coarse resolution models with three common parameterizations for mixing and deep convection with large eddy simulations (LES) of free convection in idealized scenarios. Generally, models with parameterized convection reproduce the temperature profiles of the LES reference accurately when the surface boundary conditions are resolved by the grid. Significant biases are introduced when the surface boundary conditions are not resolved and buoyancy fluxes are averaged horizontally. These biases imply that mixing depths may locally be too shallow in large-scale simulations without proper handling of heterogeneous boundary conditions during convective events; also the grid cell averaged density may be vertically homogenized within the shallow boundary layer. Adaptation of present mixing schemes may overcome these spurious effects of horizontally averaging the surface buoyancy fluxes.

Introduction

Turbulent deep convection in the ocean is driven by buoyancy loss at the surface. After a preconditioning phase, rapid surface cooling at the polar convection sites, for example in the Labrador and Greenland Seas, leads to violent and deep-reaching motion that mixes surface waters to great depth, setting and maintaining the properties of the abyss (Marshall and Schott, 1999). In other regions, for example the Weddell Sea, sea-ice formation increases the surface salinity and thus destabilizes the water column (Mosby, 1934, Foster, 1972). Numerical ocean general circulation models (OGCMs), in particular those used in climate studies, are still too coarse to resolve convection explicitly, and suffer further from a common lack of non-hydrostatic dynamics which is important on convective scales. Still the overall effect of deep mixing, namely the formation of deep-water mass characteristics, is necessary for these models to maintain realistic abyssal water mass properties and circulation.

Therefore, vertical mixing and convection in OGCMs generally is parameterized. Parameterizations include bulk mixed-layer models (e.g., Krauss and Turner, 1967), first order (e.g., Pacanowski and Philander, 1981, Large et al., 1994) and second order (e.g., Mellor and Yamada, 1982, Gaspar et al., 1990) turbulence closure models. Deep convection is usually modeled by even cruder methods, for example the so-called “convective adjustment” or increased vertical diffusivities in the case of unstable stratification (e.g., Haidvogel and Beckmann, 1999).

In polar regions, where important oceanic convection sites are located, the seasonal ice cover is a major factor determining the oceanic surface fluxes of buoyancy, insulating the ocean from the atmosphere in some places and exposing it to cold air and precipitation in others. Sea-ice formation and melting can also modify the stratification by brine rejection and fresh water release, respectively. Usually, coupled OGCMs and sea-ice models are too coarse to resolve the spatial and temporal distribution of ice floes. Instead, the sea-ice models describe sea-ice concentrations, which give the areal fraction of sea-ice within each grid box. For an OGCM this means that grid cells can be partially covered with sea-ice so that the surface boundary conditions for these grid cells are formally heterogeneous. Usually, the total surface buoyancy flux for such cells is the average over the ice-covered and open-water fraction of the cell (e.g., Timmermann et al., 2002). Therefore, high buoyancy fluxes out of the ocean over open water or increasing salinity by ice formation, which potentially could lead to an unstable water column and deep mixing, contribute only in part to the overall buoyancy flux of the grid cell, thereby reducing the potential for localized deep mixing.

In climate OGCMs, the situation may become even more difficult, because deep convection and mixing in the ocean model is parameterized. In addition to the grid-cell averaged buoyancy flux, the description of the vertical mixing is also horizontally averaged over the grid cell, thereby further diluting the impact of a localized buoyancy loss at the surface.

In this note, we present the results of a systematic study that aims to assess the effects of heterogeneous surface boundary conditions on mixing and mixing parameterizations. Due to the sparsity of ocean data on turbulent convection we choose a large eddy simulation (LES) approach, where a numerical non-hydrostatic ocean model (the MITgcm, Marshall et al., 1997) is integrated at very high resolution to simulate a convection event. The model data is used for benchmarking subsequent coarse resolution, hydrostatic cousin-experiments, also with the MITgcm, in which the convection is parameterized. Two situations are of interest: (a) the horizontal grid resolves the ice-cover or surface buoyancy flux heterogeneity and all errors can be attributed to the mixing scheme; (b) the horizontal grid is too coarse and both averaged buoyancy flux and mixing scheme contribute to the deviation from the reference. The convection parameterizations that we test here are convective adjustment, as implemented in the MITgcm, “implicit diffusion”, and the KPP mixed layer model of Large et al. (1994).

Section snippets

LES reference

The MIT General Circulation Model (MITgcm) is a general purpose grid-point algorithm that solves the Boussinesq form of the Navier–Stokes equations for an incompressible fluid, hydrostatic or fully non-hydrostatic, with a spatial finite-volume discretization on a curvilinear computational grid. The model algorithm is described in Marshall et al. (1997), for online documentation and access to the model code, see MITgcm Group (2002).

For computational efficiency we choose a domain that represents

Unstratified conditions

In the first experiment the initial stratification is neutral so that vigorous convection sets in immediately in the LES reference solution. Four snapshots of the temperature distribution after 24, 48, 72, and 96 h of surface cooling are shown in Fig. 1. In Fig. 2 we compare the different parameterizations of the convection by means of horizontally averaged temperature profiles after 24, 48, 72, and 96 h of continuous surface buoyancy loss. In the LES reference solution (solid line), convective

Idealized mixing with linear stratification

In the limit of instantaneous vertical mixing and no horizontal mixing, we can explain the behavior in the experiments with linear stratification (Section 3.2) with simple geometrical considerations (cf. Fig. 5). With instantaneous vertical mixing, the heat loss Q dt leads to a deepening of the mixed layer, so that after a finite time Δt = t  t0, the base of the mixed layer is at z = h(t). Before the cooling event, the vertical average of the potential temperature over this depth isθ=θ0-sh2,where s

Discussion and conclusion

All vertical mixing schemes used in this study reproduce the averaged temperature profiles of the LES reference runs reasonably well when the spatial variation of the surface heat flux is resolved by the computational grid. On average and especially on the 1–2 day time scales, the KPP scheme outperforms mixing by increased vertical diffusivity (implicit diffusion) and convective adjustment, which is not surprising, given the higher sophistication of the KPP scheme. With a long time step of 1 h

Acknowledgements

M.L. would like to thank Timo Vihma for initiating this study. We thank Sergey Danilov, Vladimir Gryanik, and Jill Schwarz for many suggestions.

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