Vertical mixing and deep convection are routinely parameterized in basin-scale andglobal ocean general circulation models. These parameterizations are designed towork with homogeneous surface boundary conditions for an individual grid cell. Apartial ice cover, however, yields heterogeneous fluxes of buoyancy that are not resolvedby the computational grid. The effects of such heterogeneous surface boundaryconditions are explored by comparing coarse resolution models with three commonparameterizations for mixing and deep convection with large eddy simulations (LES)of free convection in idealized scenarios. Generally, models with parameterized convectionreproduce the temperature profiles of the LES reference accurately when thesurface boundary conditions are resolved by the grid. Significant biases are introducedwhen the surface boundary conditions are not resolved and buoyancy fluxes are averagedhorizontally. These biases imply that mixing depths may locally be too shallow inlarge scale simulations without proper handling of heterogeneous boundary conditionsduring convective events; also the grid-cell averaged density may be vertically homogenizedwithin the shallow boundary layer. Adaptation of present mixing schemes mayovercome these spurious effects of horizontally averaging the surface buoyancy fluxes.