Fractional area covered by upflows of the three stellar simulations averaged over time and surfaces of constant number of pressure scale heights N_p (Eq. (11)), versus N_p. Top row: Fractional area covered by up flows from the simulations with SSD shown with a yellow solid line for the G2V star, with an orange dashed line for the K0V star, and with a brown dot-dashed line for the M2V star. The fractional area covered by upflows from the HD simulations is shown in black thin solid, dashed, and dot-dashed lines for the G2V, K0V, and M2V stars, respectively. Bottom row: Difference between the fractional area covered by upflows computed from SSD and HD simulations (Eq. (9)) shown with a yellow solid line for the G2V star, with an orange dashed line for the K0V star, and with a brown dot-dashed line for the M2V star. The shaded areas show the error of the difference (Eq. (3)). The three top axes show the geometrical height for the three stars.