We perform radiative magnetohydrodynamic calculations for the solar quiet region to investigate the dependence of statistical flow on magnetic properties and the three-dimensional (3D) structure of magnetic patches in the presence of large-scale flow that mimics differential rotation. It has been confirmed that strong magnetic field patches move faster in the longitudinal direction at the solar surface. Consequently, strong magnetic patches penetrate deeper into the solar interior. The motion of the deep-rooted magnetic patches is influenced by the faster differential rotation in the deeper layer. In this study, we perform realistic radiative magnetohydrodynamic calculations using R2D2 code to validate that stronger patches have deeper roots. We also add large-scale flow to mimic the differential rotation. The magnetic patches are automatically detected and tracked, and we evaluate the depth of 30,000 magnetic patches. The velocities of 2.9 million magnetic patches are then measured at the photosphere. We obtain the dependence of these values on the magnetic properties, such as field strength and flux. Our results confirm that strong magnetic patches tend to show deeper roots and faster movement, and we compare our results with observations using the point spread function of instruments at the Hinode and Solar Dynamics Observatory (SDO). Our result is quantitatively consistent with previous observational results of the SDO.
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