Vertical mixing and deep convection are routinely parameterized inbasin-scale and global ocean general circulation models. Theseparameterizations are designed to work with homogeneous surfaceboundary conditions for an individual grid cell. A partial icecover, however, yields heterogeneous fluxes of buoyancy that arenot resolved by the computational grid. In idealized scenarios,the effects of such heterogeneous surface boundary conditions areexplored by comparing coarse resolution models with three commonparameterizations for mixing and deep convection with large eddysimulations (LES) of free convection. Generally, models withparameterized convection reproduce the temperature profiles of theLES reference accurately when the surface boundary conditions areresolved by the grid. Significant biases are introduced when thesurface boundary conditions are not resolved and buoyancy fluxesare averaged horizontally. These biases imply that mixing depthsmay locally be too shallow in large scale simulations withoutproper handling of heterogeneous boundary conditions duringconvective events; also the grid-cell averaged density may bevertically homogenized within the shallow boundary layer.Adaptation of present mixing schemes may overcome these spuriouseffects of horizontally averaging the surface buoyancy fluxes.