tokens: between 3D and 1.5D calculations might be quite influenced by ingredients of the models that require improvement. We show the relevance of these ideas commenting on two of the few papers existing on this topic. The key is that the influence of the 3D radiation field on the Hanle polarization has been posed since the beginning in terms of inhomogeneities, and not in terms of velocity gradients. The initial conclusions in this regard were obtained by Manso Sainz Trujillo Bueno ( 2011 ) with an analytical/numerical study approaching the problem in the static regime. In more recent numerical studies the action of 3D velocities in the polarization is included, but the contributions of vertical and horizontal velocity gradients are not separated. As the effects of horizontal velocity gradients and inhomogeneities are in turn blended, it is also unknown how large their relative contributions are to the differences between 1.5D and 3D calculations. Consider, for instance, Figure 3 of Štěpán Trujillo Bueno ( 2016 ), which points out that the Hanle effect at disk center tends to depolarize when it is accompanied by other symmetry breaking effect, as happens in the well-known case of the solar limb. The figure also confirms that macroscopic motions are yet an efficient polarizing source for the spectral line considered (as known from 1D simulations of the Ca ii IR triplet; Carlin et al. 2013 ). However, it is unknown whether the polarization introduced by velocity in that figure is due to the horizontal or to the vertical velocity gradients already considered in 1D calculations. This matters not only for comparing with 1D calculations but also because horizontal velocity gradients can potentially compensate and exceed the polarization created by horizontal inhomogeneities (as explained in previous paragraphs). Thus, the dominant symmetry breaking and polarizing effect at disk center could not be the inhomogeneities, as always affirmed, but the horizontal velocity gradients. Hence, we think that is key quantifying the sensitivity of such results to the model horizontal distribution of velocity gradients , which also can help detach the conclusions from the eventual lack of realism in them. Finally, it should also be noted that when those radiative transfer simulations do not add microturbulent velocity, they use the temperature distribution of MHD models that are known to represent a chromosphere cooler than the solar one. Thus, as temperature influences significantly the effect of the velocities in the LP (see Section 4.2 ), the relative strength of the polarizing effects discussed here might change accordingly. In summary, horizontal velocity gradients compete with other physical mechanisms, such as inhomogeneities and the Hanle effect, for polarizing and depolarizing the light; hence, we need to explicitly quantify whether they are relevant for inferring magnetic fields with the Hanle effect. We also need to find theoretical and observational
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