Here we present multilevel radiative transfer calculations of the scattering polarization of neutral titanium lines in a three-dimensional model of the solar photosphere, which we have obtained from realistic hydrodynamical simulations of solar surface convection. We consider the particularly interesting case of the Ti I multiplet a{^5}F - y{^5}Fo, which is well suited for investigating the Sun's hidden magnetism via the differential Hanle effect. After considering the unmagnetized reference case, we show that the depolarization produced by a volume-filling microturbulent field with a strength such that it produces saturation of the upper-level Hanle effect leads to a much better fit to Gandorfer's (2002) observations.