Copyright © 2019 The Authors. The solar convection zone is filled with turbulent convection in highly stratified plasma. Several theoretical and observational studies suggest that the numerical calculations overestimate the convection velocity. Since all deep convection zone calculations exclude the solar surface due to substantial temporal and spatial scale separations, the solar surface, which drives the thermal convection with efficient radiative cooling, has been thought to be the key to solve this discrepancy. Thanks to the recent development in massive supercomputers, we are successful in performing the comprehensive calculation covering the whole solar convection zone. We compare the results with and without the solar surface in the local domain and without the surface in the full sphere. The calculations do not include the rotation and the magnetic field. The surface region has an unexpectedly weak influence on the deep convection zone. We find that just including the solar surface cannot solve the problem.