as well as the behaviour of anomalous refraction is much harder to measure. In fact, the anomalous refraction and its variation at small timescales is the most dominant effect limiting the quality of SDSS astrometry (see Fig. 13 of @pier03). The reason why those systematic effects could not have been properly addressed by the SDSS project itself is that the density of astrometric standards from UCAC [@zacharias13] and Tycho catalogues used for the derivation of the $(x',y')$, $(\mu,\nu)$ transformation was too low. This is where the *Gaia* DR1 comes to the rescue, with its astrometric catalogue being $\sim$ 4 magnitudes deeper than UCAC. The only issue with using the *Gaia* DR1 catalogue as a reference for SDSS calibration is that the epoch of the *Gaia* catalogue is 2015.0 as opposed to $\sim$ 2005 for SDSS and that the proper motions are not yet available for the majority of *Gaia* DR1 stars.

To address this issue, we first compute the relative proper-motions between *Gaia* and the original SDSS positions in bins in color-magnitude space and pixels on the sky (HEALPix level 16, angular resolution 3.6 deg; @gorski05) that gives us estimates of $\langle \mu_{\alpha}( \mathrm{hpx}, g-i,i) ]\rangle$ $\langle \mu_{\delta}(\mathrm{hpx},g-i,i) \rangle$. Those 