PDF of the penetration position, r_o, based on plumes penetrating at all angles and sampled at a fixed time interval throughout the full time span of each simulation indicated in Table 1. a) Penetration depth calculated from the vertical kinetic energy flux for the local convection simulations YS0-2. b) Penetration depth calculated from the vertical kinetic energy flux in the non-local convection simulations YS3-5. c) Penetration depth calculated from the vertical heat flux in the local convection simulations YS0-2. d) Penetration depth calculated from the vertical heat flux in the non-local convection simulations YS3-5. The heavy vertical black line marks the convective boundary.