Penetration of finite-amplitude columnar convection into an outer stably stratified layer in a rapidly rotating spherical shell is examined numerically. It is shown that penetration of columnar convection is not always required for generation of surface zonal flows. When the strength of the stratification of the outer stable layer is increased, small-scale columnar convection cells are trapped below the layer, but induced mean zonal flows still penetrate to the surface. Our results suggest that the surface zonal flows of the giant planets may be a consequence of penetration of deep zonal flows generated by small-scale columnar convection trapped below a near-surface stably stratified layer.